Okay, good evening. And thank you for attending the South Burlington Development Review Board of August 1st, 2023. My name is Dawn Filibert. I'm the chair of the board. And I'd like to introduce other board members, John Moscatelli, Frank Cokman. And I think Quinn Mann is online. Do we have a quorum? Yep, you have four. Stephanie's running a bit late. Okay, Stephanie should be here any minute. Marla Keane and Marty Gillies are our staff members. And thank you for all coming. We are recording this meeting. And there are a number of ways of participating. You can either come in person and you can attend virtually or you can call in. And whatever way you attend, it's important that you register your participation by either signing the sign-up sheet at the back of the auditorium or on the chat function, give us your contact information. And if you're calling in, you can email your contact information to mkene. SBVT.gov. And that's Marla's email, so that we know you have participated should you wish to take any future action as a participant. So our first item of business is emergency evacuation procedures. In the event of an emergency, there are backdoors at each corner of the auditorium. You would exit those and go either left or right, then you would be outside. Are there any additions, deletions, or changes in the order of agenda items? Nope. Are there any announcements? Last meeting, the board asked me for an update on the DRB vacancy. Jesse, let me know that council has decided to combine posting the DRB vacancy with two other vacancies this month to do appointments in September, either at their September 5th meeting or the September 18th meeting. They have also authorized us to have, to invite an interim member, someone who's been on the board before. So I'll talk to you guys about whether you wanna do that during deliberations later tonight. Good, thank you. Any comments and questions from the public that are not related to the agenda? Hearing none, we'll move on to the first project. Agenda item number five, site plan application SP 23031 of Craig. We linger. Am I pronouncing that right? We linga. We linga. We linga. Thank you. To amend a previously approved plan for 5,620 square feet, for 820, 5,620 square foot place of worship. The amendment consists of fill removal, exceeding 20 qubit yards and associated regrading for the purpose of stormwater management in the rear of the property and minor site improvements at 12050 Spear Street. Are there any recusals or disclosures related to this? Okay, who is here for the applicant? And your name? Craig. Craig. And are you the only person here for the applicant? No, got Art and Ed. Art and who? Ed. Ed, okay. Ed Darling. Okay, thank you. And we could get you all to sit up at the testimony table. There's two mics there. And if a third person wants to testify, you can stand at the podium. The mics, there's a little button that says push and the light will turn from dull green to bright green. And you want to pull it very close to yourself. Could you all raise your right hand please? I'm going to swear you in. Do you solemnly swear to tell the truth, the whole truth and nothing but the truth under penalty of perjury? I do. Thank you. Okay, welcome. And we have your application. And before we start to go through it, are there any introductory comments while I look for it on my iPad that you would like to make? No. No, okay. Give me one minute please. Earth did this. Hold on just a second. So what we have for this application, which happens but is not the most common, we actually, instead of a staff report, we have a draft findings of facts and conclusions of law. And we'll go through that and see if the board has any questions or comments. And then hopefully conclude the hearing and close the hearing. So my first comment is on the third paragraph, Marty. Is this yours, Marty? Yeah. I think there's a based on testimony provided at the above mentioned public hearing. I think it's a singular. Oh, sure, yep, thank you. And I don't think, maybe I do have other comments. Any general comments or questions from the board before we move into the red comments from staff? Okay, on page five, there's a question of whether we should continue this hearing or have a condition that the stormwater superintendent review and approve any applicant response to the provided comment. Are we all comfortable with that condition? Yeah, I can jump in on this one. So a little bit has happened since I published a staff report. At the time, Marisa, our stormwater superintendent made some comments, just some minor edits to the EPSC plan and the grading plan. The LDRs give the board the authority to impose conditions of approval, but not conditions of approval that leave any part of their implementation to the discretion of the applicant. So they have to be very, very specific and prescriptive. And often we just say a condition of approval might be comply with the comments of the stormwater superintendent, but Marisa's comments were quite vague because she was trying to give Craig the bandwidth to do the right thing for the site. She didn't want to be too specific. So it kind of left us in this weird catch 22 where the board couldn't approve a condition that was so vague, but Marisa couldn't make the condition any more specific. So it was kind of circular logic there. And luckily Craig and Marisa were able to carve out the time to hammer this out before tonight's meeting. So today I got an email from Marisa saying that, and I also got the revised plan. Now plans that are approved by stormwater that just make them in this packet. So that will actually appear in the conditions of approval? My recommendation now, as of like one week since I wrote the staff report, is just that the DRB have the applicant comply with the comments of the stormwater superintendent because they are now specific enough. Perfect, okay, good. Thank you, Marty. Any questions in the board? Good, okay. Then there's a placeholder for that. And I think that's it on comments from staff. Any questions from the board before we close this? Yeah, so we did have one public comment from the University of Vermont and they just submitted it via email. They couldn't be here tonight. It's brief and I figured I would read it if you guys don't mind. And then we'll take any other public comment. Sure, yeah. This one says, as the stormwater flows from this project, being the one on the church property here, are directed north to the university's Witless Sea Tract. We, being UVM, offer the following requests for mitigation to assist in maintaining the current runoff conditions post-development. And there are two. One, UVM requests that a level spreader be placed at the daylight end of the drain pipe that collects the downspout on the south side of the church roof and that at least 15 feet of vegetation be maintained between the pipe outfall and the top of the swale for runoff disconnection. And then number two, UVM requests that dense vegetation be maintained at all times for runoff disconnection between the east side of the new sidewalk and the swale. And they finished with thank you to the members of the DRB and to the Episcopal Diocese for considering these requests to ensure that these changes do not increase the runoff flows onto the university's property. Thank you, Marty. I assume you've seen this. Yes. And are you fine with those conditions? Yes, I think that they should be, we should be able to meet those satisfactorily. Great, thank you. And are they built into this decision as drafted? They're not, no. But we will, they will be. So they should be, right now. Sure, yeah, we can. If you feel that's appropriate, we can edit the draft decision to include those comments of UVM. Any other comments or questions from the board? Any other public comments? Hearing none. I would entertain a motion to close this hearing. So moved. Thank you, Frank. Second. Thank you. All in favor of closing the hearing? Say aye. Aye. Opposed? Aye. Okay, the hearing is closed. Thank you. Thank you. Next on the agenda, preliminary and final plat application, SD 2311 of Casey Douglas to amend a previously approved 5.52 acre, six unit plan unit development. The amendment consists of subdividing lot six developed with a single family home and barn into two lots of 0.69 acres, lot six A and 0.60 acres, lot six B for the purpose of demolishing the existing family home and barn and constructing a new family, a new single family dwelling on each lot at 1200 Dorset Street. So if you just bear with me, while I find this on my iPad, are there any disclosures or recusals? Hearing none. Who is here for the applicant? A familiar face I might add. Too bad for you. I'm Dave Marshall from Civil Engineering Associates and I believe remotely, we also have Casey Douglas, the applicant. Okay. I am here remotely, yes. Okay, great. So before we start going through the staff comments, which mostly are like, do you agree and can you comply with X, Y and Z? Do you have any comments to make? No, we're very happy with moving through the staff comments. Okay, great. Thank you, Dave. All right, it's not numbered, but the first comment, we do, thank you very much. I'm gonna swear you in. Even better. And Casey, please. Thank you, John. Do you solemnly swear to tell the truth, the whole truth and nothing but the truth under penalty of perjury? I do. Thank you. Thank you. Okay, I'm gonna read this. Staff recommends the board include a condition that the development on each of the proposed lots meets the dimensional standards of the Southeast Quadrant Neighborhood Residential Zoning District. No issue there. Okay. Okay, moving on. Staff come, I guess that was number one. Staff comment number two. I'm gonna read this. Staff recommends the board direct the applicant to address the comments of the Department of Public Works Director prior to closing the hearing. And they're all there in the staff report. There will be a number of public works issues that come up subsequent to this one. So the answer is that's acceptable. Okay. We will work with public works to get them up to speed with what the plans indicate or don't indicate to allow that item to be addressed. Thanks, Dave. So it sounds like we're not closing tonight. We're just concluding and continuing. Unless you, based on Marty's point in regards to conditions and openness or lack of openness, that's open as far as how the board would like to handle it. The applicant would love to have a closed hearing but the reality is is we need to make sure we're all on the same wavelength as far as the issues and we can provide appropriate information for the board. Great. Okay, thank you. Number three is regarding the water pressure and ensuring the adequacy of water pressure. The staff recommendation is to work with the Director of Public Works and South Burlington Water Department, superintendent to ensure that water pressure will be adequate for the proposed homes. Not an issue. Actually, this subdivision is serviced by the Vermont National Country Club water distribution system that was specifically designed to handle the high elevation buildings. This is in the low elevation portion of the property. So the Public Works Director may not have understood that that particular relationship because otherwise just being serviced by the water tank across the street may put you right on the edge. So in this particular case, as part of the original subdivision of Paul Heald, there was an agreement with Vermont National Country Club to be serviced by their particular water system. Okay, good. Any questions, comments? I kind of have a question. Sorry to jump in where it's not my turn but is that a private water system or is that just like a booster? It's a booster that is a private system that is operated by the South Burlington Water Department. But it's municipal water. The water comes from the city of South Burlington, correct. I should learn more about that. Thanks, Dave. We're happy to fill you fill in the blanks. All right, yes, sure. Frank. Let's run through that one more time and say, the water is South Burlington municipal water. Correct. But it's a private system and the private system is operated by the city of South Burlington. Under contract. Who's the owner of the system? Vermont National Country Club, Highlands residential development. So the background, Frank, is before they raised the water tank on the street there that the highest portions of the Vermont National Country Club did not have adequate pressure through standard distribution line feeds to that area. So in order to mitigate that, there was a proposed and ultimately permitted and constructed booster pump that takes the water from the municipal system, adds energy to it, pressure, and then redistributes it through the water distribution system in the streets. Is the country club, what is the relationship between the country club? I assume that's a corporation. Yes. All right. So it's the corporation that owns the system. They own the booster pump station. The city owns all the mains within the streets. Anything that deviates out. But the booster pump station is owned by the corporation. That is correct. And the system serves, the system that gets the benefit of the booster serves private homes. Correct. That are located within the Vermont National Country Club and through special agreement. When you say within the, and I need a little education on what those relationships are. To private homes within the Vermont National Country Club. Is that a big PUD, the Vermont National Country Club? What is that arrangement? It's multiple PUDs within the country club master plan. Yeah. Okay. Of which this PUD is a part. Okay. So the relationship between the corporation and the owners of the home is, and the owners of the private homes is what? Yes. So, big picture. Vermont National Country Club, we'll call it master planned community, has residents that benefit from this particular water distribution system. And separate of that entire original approval from the city in 1997, is a separate subdivision created in 2000 that through a sub-agreement with the Vermont National Country Club large development project, benefits from water distribution of that water booster pump station. And this project will have exactly the same status in relation to the corporation as the private owners do or not. That's my understanding. Okay. That's what I'm trying to get at, I guess. In other words, there are no more at risk of losing the benefit of the properly pressurized water than the residents of Vermont National Property. I think that's a fair representation. Thank you. Thanks, Frank. Any other questions? Okay. Number four, staff recommends the board direct the applicant to address the comments of the South Burlington Water Department superintendent prior to closing the hearing. Comments four through 13 are standard comments and no action is requested. Right. So items one through three actually stem from any typo on our plan. So we will correct that work with JNATO at the water department to allow them to understand exactly what is out there as far as an as-built condition and how it will service the two houses. Good. Thank you. Number five, this is the fire marshals comments. Yes. There was a little bit of confusion, Marty, with regard to the specific call outs of 6B versus 6A as far as the lots and what the fire marshal was intending. So the only way for us to all understand perhaps what he's talking about is to bring up the site plan that shows the two lots and their specific numbering A and B. So keep in mind that this note talks about lot 6B being more than 150 feet away from Folsom Hollow Road and he may have meant 6A. So the opposite lot. Okay. So once we bring it up on screen, I'll kind of do a paraphrasing of my understanding of the fire marshals comments. Yes. I agree. Okay, this one's kind of hard to read but it is in the application package. Let me try for the other one with the aerial but I'll pause it while it loads and then keep going. So in this particular case, lot 6A is the Nordely lot and 6B is a subtlety lot. And the fire marshal provides comments that indicated first questioned whether the curving driveway was A, a common driveway. The plot plan actually shows that there's an access easement to enable the rear lot to access Folsom Hollow Road through that common component. And so there's a question of way can I get my equipment back there? And then two, the next question was, well, 6B seems to be more than 650 feet away from Folsom Hollow Road and Folsom Hollow includes the cul-de-sac that's before you. And we were actually wondering if lot 6A, which is the North lot, is the one that seems to fit the bill better. So if it is either way, we still need to talk to the fire marshal to come to agreement on how to address his NFPA one requirements as far as access with the understanding and the frustration that if it wasn't for a common driveway, he would be able to respond either from Dorset Street or Folsom Hollow Road with some hose. But putting that aside, we will work with the fire marshal on that particular item. Great. Okay, thank you. I again have a, forgive my lack of understanding, what's a NFPA 13D sprinkler system? So National Fire Protection Association is a group that tries to create standards for applications throughout the country. As far as how to deal with emergency response, fire response, 13D is a type of sprinkler system.  Let me short circuit it. So it's a sprinkler system like any other building sprinklers. It's in the house. It is in the house. Okay, so what's confusing is the lot. So when any house built on the lot will need a third, not the lot. It's not the lot that needs the sprinkler system. It's the building. It's the building, okay. That is correct. And just for the sake of English, maybe we should specify that in the agreement. Excuse me, in the permit, right? It's a widely accepted set of standards, National Fire. It is. Yeah, I see Dave's point. I just did these quick little measurements. It's 75 feet to the home from the, from the Folsom Hollow and 80 feet from the home to North Street. So I think that they're thinking that they're going to have to access it via the driveway. So it makes sense, Dave's point that they should just talk to the fire marshal. That's probably the most expeditious way of scanning this. Give a little to-do list. Understood. Okay. Number six, address the comments of the South Burlington Stormwater Superintendent. So this is probably the one we do take issue with in the sketch plan application. The directive from the stormwater section was that if you were going to create more than one half acre of impervious area on your subdivision, then you were obligated to comply with the requirements of section 13.05. Subsequent to that, the application morphed to the point where we started to describe it as an amendment to the PUD, which in order to basically keep the house cleaning, housekeeping squared away, that's fine. Our frustration is that the actual wording in 1305 is when the applicant comes forward with a subdivision and the amount of impervious area on their property is 13.05, excuse me, more than half acre, then you need to comply with these rules. Our frustration is that these particular public work standards, or I'm sorry, the stormwater requirements within the land development regulations were put into place after that original subdivision in 2000 was created. So we're feeling that we're getting penalized for after the fact, oh, by the way, you're part of a subdivision and in this particular case, applying rules that weren't in place for the original subdivision to this little 1.2 acre piece. You're changing the subdivision. We are. You're changing the subdivision after the rule was changed. I don't have any problem with addressing that for the portion that we're changing. We're not changing any of the other lots that have been there nor the street that's been there for a long period of time. But you're causing the overall impervious to exceed the permitted maximum, correct? Not the way I look. So what we want to do is recognize that when the rules came into play that anything subsequent to that needs to comply with the rules. And what we're saying is that this subdivision predated any of these standards and that we shouldn't have to go and retrofit the entire subdivision. I'm sorry, I understand your argument, but I think it's specious. I don't like that word. That's serious. Frank, please. I think it's wrong. Okay, that's fair. I'll take that. I don't like the other word. So that being the background, we will take that up with staff for further review as far as how to apply that particular requirement. I'm just taking the word specifically right out of the regulations. Okay, thank you. Any other questions about that? Thank you, Dave. Can I jump in for a second on that one? Sure. Just to clarify a point. So the way I read that is that the applicant is required to provide stormwater treatment for the entirety of new and redeveloped impervious just on lot 6A and 6B. Correct. Okay, and then you were mentioning the rest of this subdivision in the context of stormwater treatment. Correct, because the comments came back different in the sketch plan. It basically said, if your project, the two lot subdivision has more than half acre then you need to comply with 1305, which is fine. And we said at the time, well, we don't. We're not anywhere close to meeting that standard. However, it came back differently from Marisa in this case that basically said, oh gee, now we're talking about a PUD, which is what Frank is kind of pushing, which is, you need to basically take everything into account, which would be fine if everything was applicable to the rule if the stormwater rules were in place at the time of the original subdivision. This is kind of a timing issue. And specifically what is happening with this applicant's property. So that's the wording in 1305 is the applicant's property that comes before the board. Tell us about your amount of impervious service that you're proposing, whether redeveloping or otherwise. So that's our position. And we will work that out with staff further before we take any more of your time here. I would point out that it's very common, particularly with environmental regulations at the state level as well, that you get a pass on whatever conditions exist as of the date that a new regulation is passed. But when you make a change, you need to comply. And here what I'm saying is you can't close one eye and pretend that this little subdivision within a subdivision is not a part of the whole. And he says, yes, you can. So let's see what kind of how we can work this out or how you can work this out with staff and we will be seeing you again. Very good. Okay, let's see, oops. Number seven, I'm gonna read this. Staff recommends the board require the applicant to demonstrate how the required area of civic space or site amenity can be provided with the proposed subdivision by designation of such area on the proposed plans. Very good. So question is, is this a two lot subdivision or a seven lot subdivision? And now it becomes convenient to have it be a seven lot subdivision. No, not really, but nonetheless, if we're talking about, so the regulations require that for each lot, you're required to provide 100 square feet of amenity space. So staff is identified and actually when you go through all of the various tables that for small subdivisions of this particular type, even if you include the other lots, we're still less than 10 lots and that it requires 200 square feet and it ultimately indicates that it's essentially just needs to be open space or help us out there, I'm already. Yeah, our thought, our consideration was that private yard is an acceptable site amenity and so it's really just a matter of designating private yard space on the plan, identifying that the units all have the required minimum square footage of sedimentary, in this case, yard space. Okay. And we. It seems too easy, but nonetheless, it sounds like we need to identify that in order for the lot to be considered to be complying that we need to ensure that there's 100 square feet of, sorry, just lost the word for it, private yard space on each lot, which I think is kind of a no burner when you look at the lot size and how to apply that, that's fine. So we will add a note to that effect. Yeah. Okay. Great. Good. Thank you. Problem solved. Number eight, this addresses the, this is about addressing the comments of the city arborist. Sure. So actually in our cover letter, we talked about the landscaping plan in which we had identified on one particular plan, those trees to be removed. We have a landscaping plan that shows all of the trees to be retained. And we have an EPSC plan that shows how those trees are to be protected. But if we're going to basically take a time out, we will go back to Craig Lambert and make sure that he understands that the information is all there. It's just in three different places in order for him to feel comfortable that he can clear this for you. Okay. Great. Thank you. So Dave, I saw the landscaping sheet and the EPSC sheet and the third one you mentioned was? I think it was, hold on. So sheet C1.0 shows the existing trees with call outs and those to be removed. So you've got three sheets. C1.0, 1.1 is the landscaping plan, which essentially is retaining, there's a lot of screening trees out there today that shows all of those to be retained. And then specifically on the EPSC sheet, excuse me, it shows those particular tree protections. I think it probably in confession, it can be cleaned up a little bit on the EPSC sheet to make sure that the tree depiction is more clear. Great. All right. Number nine, this is about the roof line, pardon me, facing south to maximize solar gain. Just an editorial based on how the applicant worked with the board as far as how to orient the buildings in a way that makes sense with the fact that one of the buildings has frontage on three sides. I think that's fine. We're finding that in our work on solar that there are parts of the country that require that the roof's face west because they're interested in picking up the peak hour generation. And what that does is eliminates the need to store during the middle part of the day when the sun's coming directly out of the south. So just an editorial in regards, but your regulations specifically talk about or infer that it should be to the south. So in this particular case, the answer is easy only because of the other requirements that we have within the LDRs. So the answer is it's a reluctant, yes, we can live with that condition. Okay. Questions? I'm with a developer on this one. I think that ought to be flexible for the developer's benefit. I don't, it doesn't seem to be a locked in stone benefit is the point. Well, it does say orient to maximize solar gain potential. It doesn't say orient to the south. Good point. So there is some flexible language even in within LDRs and sometimes you wish for more definition here. I think as Marla made me point out, I was Frank's pointing out that as times change we realize there have different goals in regards to how to deal with solar that perhaps that statement allows for that. So we're open only if our buildings were oriented differently, we might be having a bigger discussion. We're at the whim of the board as far as how you would like to handle that. Thank you. So the next couple of comments relate to the architecture. I'm going to read number 10. Staff recommends the board require the applicant to enumerate to what characteristics of the conceptual homes the applicant proposes to commit in order to ensure future compliance with this criterion. And I know Mark our architect is not here with us tonight but this is really about getting more specific about what we can count on for you to do. All right. So within the application package there were some likenesses, some of them will actually represent the applicant's proposed home. So in this particular case, one of them represents essentially what if everything were to go well as far as approvals that you would see constructed. The second home, the Southerly Lot 6B is one that doesn't have any immediate plans. And in this particular case, what we've tried to do is identify at least the character and the specific question is as well, Dave, what specifically are you willing to? Commit to. Commit to be committed, maybe, but no, commit to. And we did that with the specific call outs on that particular graphic, for example, as far as features that we were looking to ensure that anything, any future building would include those particular characteristics. Can you clarify which is the one that's what they actually intend to build in, which is the one that is a conceptual one? Or are you saying both are conceptual? 6A is more, how do we wanna say? I don't wanna say more real but is probably more representative of ultimately when a zoning permit would be submitted that that's what you would see it as part of the application. Okay, but neither is a full commitment. They're both conceptual to a greater or less degree. I would love to say yes to gain flexibility, but at the same time, we also wanna bring closure to this issue for the board. So that's where, again, I apologize for being a civil engineer but my brain stops at the outside of the building. So I wish Mark, we're here to give me more support in regards to exactly how we want to work our way through the vertical components of these structures to make sure that the goals and intents of the Southeast quadrant are being met. So that's the statement. I don't know if I have a real answer for you yet other than the fact that the call out specifically are things that we will be, are committing to and that's why the applications materials are reflect those specific pieces of information. We do have four plans that technically are required as part of the submittal. Again, kind of wondering how you wanted to understand what's going on inside the building, but that's an editorial, we'll move on from that. But again, in order to complete the application, that information is in there all. My let me understand this is the application before us is strictly for the subdivision of the lots, right? So let's hypothetically we say yes, go ahead and subdivide. We have no, to what extent do we have any continuing control over the design of the houses themselves? I think that's what we're trying to sort out. So that's the standard. It's the standards about relationship of structure to the site and harmonious relationship to the brain, pattern and rhythm, architectural features, privacy. I guess that's right. So the idea here is within a PUD these standards exist. And so Marty's suggestion in this comment is, okay, we understand that they're conceptual elevations, but what elements of these conceptual elevations make it so that these criteria are met and the board feels like the applicant ought to lock themselves into. And so what Dave is saying is we are willing to lock ourselves into these things that are called out with the blue in order to meet these things. Rhythm of the site and harmonious relationships and screening and architectural features being responsive to the neighborhood character. Would you be willing to say we will build, the structures on each lot will be substantially the same as those presented as conceptual drawings, except as the board may allow through future amendment. That's fair. I think that's awfully specific.  And I think this was one of yours. Bitten the butt on what I just said? Yes, because if it's conceptual, and then, you know, they decide they want to do something else, then it's a whole public hearing for what would otherwise be a single family home approved administratively. Well, exactly. But if we don't do that, then they... Well, so they're proposing to commit... A skate for lack of a better word, a skate for the application. Well, they're proposing to commit to certain elements. They're proposing to have a setback garage. They're proposing to have a covered front porch. They're proposing to have a dark color single roof on this home and on the other home. They're proposing to have these four things, that the garage is a side facing garage. They want a front porch facing full Schimpolo. They're gonna have a exposed foundation. They're gonna have a pitched single roof and a dark color. Are those things enough? Or does it also need to say, you know, it should have a large percentage of the facade having windows that are taller than they are wide or the siding shall be generally horizontal. You know, because if you had a modern looking home with vertical siding, it would look out of character with the neighborhood. It shall have a pitched roof as opposed to a flat roof. So why don't you get that by being substantially and substantially in accord with the elevations and renderings presented to the board? Well, who decides what's substantially? Well, there's a slippery slope. That's not a very slippery slope. Well, here's an option. And this puts more pressure on staff, but an initial determination can be made by staff. And if the staff says it's a nice tri-day, that's not what we think is appropriate.  Is that a fair representation of the process? You mean the denial of a zoning permit and subsequent appeal? I don't wanna set it up for that. You know, my concern is that we decide it's substantially similar and the neighbor says, I disagree, it's not substantially similar. I'm appealing this to the DRB. Why would we be intentionally setting ourselves up for appeal? You know, I guess I'm kind of used to substantially similar as a standard. It's a not uncommon legal standard and it's not as slippery in a courtroom as it sounds to you. I mean, we're happy to enumerate the things that Marla just mentioned, and I think in the future, even if it's just a worksheet that staff can share with applicants to say, hey, touch base on each one of these things, it makes it easier for all of us to understand what you're looking for. Because right now it's hard to commit to something that might not get built for, who knows, 15 years. So you could say substantially similar to the renderings presented in particular and then provide your list about that. Okay. Yeah, and what's substantially similar may vary by neighborhood. If this were... Yeah, what we're talking about... If this were the, what is it called, Queen City Park neighborhood, there's a lot of very modern homes. So vertical siding and flat roofs might be more characteristic. We're saying it's substantially similar to the other houses and the developments, right? I think that's what the regulations say. It's in the neighborhood. Right. It essentially is off a portion of the road. Seems like we're trying to avoid putting up a center hall colonial next to a craftsman style next to something that's very modern and having a very eclectic mix. Not that that's necessarily always bad, but it seems like the standard of looking for is that you don't end up with something wildly modern next to something very traditional. I wonder if we could do this so we could end it at this level. Have these guys come up with their list of specifics and negotiated with you? Because we're not gonna close this tonight anyway, I don't think. Well, I feel like, I mean, I don't disagree, but I feel like between Marla and Marty and Dave, they've identified kind of the common elements that would pertain or apply to both of these structures. And then within that some flexibility. So I'm quite comfortable with that. So I have a radical idea. Because everyone just laughed when John talked about having it being an eclectic mix of homes, how like that's not really a bad thing. These are the standards. Having transitions between buildings of different architectural materials or harmoniously to the terrain, is it fair to say that a single family home is sufficiently similar to an adjacent single family home that nothing more needs to be said? This is a totally radical idea. But if it's a single family home, how dramatically different can it be from any other single family home? Very. And is that what this standard requires?  No, no, no, this is useful because this one is very frustrating for the left brain engineers, say, you're asking me to commit to something in the future that I have no control over other than through this particular process. And how do we hamstring somebody in the future who might be Frank Lloyd Wright architect who says this is a wonderful feature based on the landform, but it doesn't look like your neighbor's house. All right, and does that, my question is does that, is that what's required? Is it required under this LDR to make the houses look like the neighbor's houses? Or is it being a single family home sufficiently similar? And is that a question we should throw back to the planning board?  I agree with that, and I'm a different kind of engineer. I have, you know, I would look at that and think, wow, we really ought to have an architect. Should I mic on for Quinn? Sorry about that. That we really ought to have an architect define some of this stuff. Okay, if I just assume you had those renderings, are they stock images or was there an architect involved in putting them together? I'll answer John's questions first. It started out with stock, one of the two is stock. The first one for lot 6a, the northerly one, is one that is now being developed by an architect. Because I'm just saying you could probably have your architect look at it and come up with some typical architectural features. And they'd probably get into stuff that we're not thinking about right now with patient soffits and overhangs and fenestration and all kinds of stuff like that. And Mark would probably agree that that's how you should define it. And that might be a way to do it is just have your architect say, any little thing that we build is going to be in this style. And I think that works well for lot 6a. 6b doesn't have an architect. Or if you were in a situation where there were no architects involved at all other than the left brain civil engineer trying to draw lines for a subdivision, is like, well, how do we create the character, how do we describe the character of this neighborhood that isn't even there perhaps yet? Right, Frank, I know you wanted to say something. Well, keep in mind it's up to us to interpret the meaning of the line, which in other words, it's our judgment. What is harmonious is not a precise scientific or expert judgment. It's committed to our discretion because that's the position we occupy under the legal structure we're in. So when it says proposed structure shall be in the opinion of the DRB unfortunately and to sometimes to the regret of the developer. Harmoniously, related harmoniously to themselves, this terrain and the surrounding buildings or the existing buildings. And that's why I come back to my first point. We see something, we've seen something, we like it. It looks harmonious to us. Let's say, make it like that or come back and ask for a change to show us something else that's harmonious. To me, it's not rather than a list of elements, you know? I'm following your lead only because you get to do the heavy lifting as far as least providing an interpretation. And then out of all that, once we understand what your expectations are, then our job is to fill that. And right now, this is one that seems to have been, it's been batted around. So let's move on to number 11 because I'm frankly not clear how this is all that different from number 10. It's not entirely different. It's just a similar standard. And therefore requiring similar board input on whether that standard is met. So in that one, I had sort of suggested, considered that as we're looking for not cookie cutter homes like not a particular architectural style as it says in the language there but more of features that define the neighborhood character. And so some that I had picked out in my comment there were the two-story dark roofs, attached multi-car garages as opposed to detached, kind of those seem to be the things that generally broadly define that neighborhood without locking the applicant into anything too crazy, especially considering that they proposed two-stories attached multi-car dark roofs didn't seem like a huge jump to me. So that's kind of how I interpreted that second one which is granted a little bit of a simpler regulation as opposed to that first one. Something else just occurred to me.  Proposed talk show shall be related to harmoniously. Then you come for the zoning permit and the initial judgment. Looking at it, I'm withdrawing what I said before. The initial judgment is the zoning administrator's judgment. Well, your permit says it's got to relate harmoniously, blah, blah, blah, and the rest of that. And the zoning administrator thinks it does. So the zoning administrator issues a permit and that's that. The zoning administrator, or a neighbor, or a neighbor, somebody appeals it. Well, the zoning administrator thinks it doesn't, in which case we are the ultimate deciders of what's harmonious, but from an efficiency standpoint, and I don't think it does any violence to the ordinance to say the first call is the zoning administrator's. The requirements that it relate harmoniously, the judgment in the first instance lies with Marty or whoever's in his shoes, and the appeal is to us. How's that sit with you? The standard says the development review board though. Does it not? Well, look, either you lock in now and we say it relates harmoniously and you've got to come to us or amend it. I'm trying to give you a way out of that, of that, of that.  And what I'm seeing here is an extension of those particular standards with more detail that basically says, well, beyond just what the location and shape and height of the building is, we also want to make sure that there's these other features that are embedded into your application when you come for a building slash zoning permit. And this is what we want you to comply with. And so I'm following Frank's lead, which is, well, it puts a lot of pressure on the zoning administrator to basically interpret what's happening in the neighborhood and whether or not this particular proposal that's before them for a building permit slash zoning permit is indeed compliant with the rules. Back in the days when everything was left in easy numbers, it was an easier job. When you now ask for some sort of subjective component, which again, people are strong and weak, depending on how you want to interpret something is the challenge. And that's why I think staff has always said, gee, Dave, can you at least write something down to give us a little bit more framework on how a future application would come before the zoning administrator? So that's kind of my take on how things have evolved and how they could either be straightforward, put everything in the zoning administrator's court to determine that it complies with the LDRs, or is it one with a little bit more framework based on what the creator of the subdivision is willing to commit to? So I have a suggestion. We know we're not gonna close tonight. So could you and Marla and Marty kind of put your heads together and come up with language that you think we can subsequently review and live with, finding that common, I mean a kind of a midpoint between being too prescriptive and yet giving us enough specificity that we feel comfortable? Well, I'd like to know the temperature of other members of the board. Are we looking for relatively locked in somewhere in the middle or if it's a single family home, it's close enough? Single family home is not close enough. Others? There's all sorts of single family home. You could have a ranch house for God's sake. But actually, if you look at one at the bottom, reading the whole thing through, buildings of different architectural styles. So it already accepts that the buildings don't have to be the same architectural style. The whole pattern and rhythm thing, that sounds like the top of the screen. One, you get down to the bottom of it between buildings of different architectural styles. So you can have a contemporary and a traditional building, but somehow you're supposed to make the landscaping, make them look harmonious. As if the pattern and rhythm sounds like setback, front setback, side setbacks, that sort of thing. You don't want one right next to the curb one. But that's all handled elsewhere. You can't do that and follow it. So I personally am quite confused as to what the intent of this was. It almost seems like a lot of very loose language to give us a lot of authority to say, we don't like that, don't do it. Which, I mean, I don't write it and it's not my job, but I don't think that's the function of government. I would be more, Marla is saying that if it's a single family house, it's a single family house. It's make it look nice. You're gonna try and sell it to somebody anyway. So- Sure, it's in everybody's best interest. As long as you're following all the bulk requirements and it's got a garage and a roof, I'd be okay with it. I agree with that. Well, you're looking at one, but then there's two. You have to read them together. Related harmoniously to themselves, the terrain to existing buildings and roads in the vicinity. Right. Can we hear from Quinn on this thought too? Sure. Quinn? Yeah, thanks. I was falling somewhere more in the middle. I think we're not just the single family home, something a little bit more. On the detail, the items that the applicant has put forward so far, at least to me on this, I'm not sure how they relate to the other structures. So if items are put forward, also along the lines that I think Marla put forward, as far as the color and the direction of the siding and such, just making that more clear that that's consistent with what's already in the neighborhood, because based on what the applicant called out in their concepts, it's unclear to me that that's consistent with what is also in the neighborhood. So that makes sense. Thanks, Quinn. That's a good point. So is that the homework to demonstrate that the things that are being proposed is consistent? Mm-hmm. I think it is. So let's move on to number 12. This is around orientation architecture again. A staff recommends the board discuss whether they are satisfied with the proposed orientation of the proposed homes, indicate whether those proposed orientations are acceptable given the criteria outlined herein. Right, so in this particular case, this is what we spent time discussing this at the sketch plan. And it's our opinion we took your thoughts and guidance and put them on the plan. One of them was to, on the southerly lot 6B to change its locations that it wasn't gonna be as much earthwork necessary in order to basically enable the layout on that particular area. So that's fitting with the land as far as that particular end of things. There were also issues with that lot 6B because it's got three frontages, you know, one on Dorset Street and then of course Folsom Hollow that circles around it on two sides. So three of the sides essentially had front yard and you know, when we talk about buildings and how they communicate with the streets, the question was, well, how are we gonna make this one communicate on three sides? And the decision was we would have the primary entrance off of Folsom Hollow Road. We would create a basically a backyard porch that communicated with Dorset Street and the recreation path and that the existing landscaping on the south side essentially was a wonderful screen and that we wouldn't try to do anything on that side of the building. So that's what we took out of the SCET plan hearing as far as the concepts and that's what we've embodied into that particular layout. And this would be one of those commitments we need to basically write down is beyond what the site plan might be able to say, but it would be good in writing to identify those as specific features for that particular building. Thank you. Comments, questions? No, and maybe far too late to say it, but I've noticed on Dorset Street how many buildings there are with their back porches facing Dorset Street and I don't think it's particularly attractive. But that's what we've required. We've required or allowed. That's what my understanding that's what the LDRs call for. So no, it requires, so in my time here, the board has required homes to have a facade that faces Dorset Street or something that is somewhat facade-like facing Dorset Street. And I think that's a response to how many of the homes have their backs facing. Yeah, so the question I had for you is, I see a little bit of green along Dorset Street. Is that just the color you just decided to use to outline the lot or is that vegetation? Is that some kind of screening? So the yellow, it may look green on your screen, just represents the property lines, Frank. But there are a number, for this ortho-photo, there are a lot of trees either with green or black shadowing based on the direction of the sun that are all existing and if they're depicted on this particular plan, those are the ones to be retained. How high is that gonna be, the green, the green? Is it gonna amount to a buffer? In other words, is it gonna shield the back porch from visibility on Dorset Street or candidly not, probably not? So there's one deciduous tree between the street and that backyard area. And I guess the question is, my understanding is that going back, even before Marla was one of the goals was communication. You wanted to be able to sit on your back porch and when somebody walked by on the recreation path, be able to say hello. So... That's not what's happening on Dorset Street. I'm just saying that was the goal. And that's essentially what is created here. So hiding the building from Dorset Street doesn't seem to be consistent in that particular communication component. So that's at least my take and experience in working with the city since they adopted the traditional neighborhood design. I won't take more time. I don't think the board's precedent would allow for making that any kind of determinative objection. Okay. I'm just our experience. Okay. Any other comments before we move on to 13? Okay. This relates to what elements to retain and the end of the staff comment is, which elements of the proposed elevations the applicant must retain in order to ensure compliance with this criterion and include such elements in the decision? I think we've covered that and I think you're gonna work on that. Yes. So thank you. Moving on to number 14 is the timeframe. And I guess I'm really puzzled why 6B could take five to 20 years. So these lots are being created for family members. So a sister and a brother are gonna own the lots. The sister Casey Douglas is looking to build her home as soon as possible. So the 2025 number that's in the it was reported in the application is an overly conservative estimate of how long it'll take to complete the home. So they are very committed to moving forward with the Nordely lot as far as construction. Southely lot. The brother said I got a home not interested in doing anything right now. I have no idea when my plans to do something would be. So that's the dynamic of how this particular narrative is coming forward. Okay. Thank you. Comments. On that particular point. Well, so there's this housing preservation standard. I don't know if Marty you wanna kind of go into that. What is that? I wanted to play. It's new. New and improved. Not that new. So if I can paraphrase and maybe I shouldn't but Marty and Marlon probably are more close to this is possible. The goal is to basically make sure that we're not tearing down buildings and losing housing stock and converting them into things that aren't consistent with the overall goals of the city. So in this particular case, there is a home that is falling down. That is essentially condemned. But at the same time, the rules specifically say, hey, it doesn't matter whether it was the previous owners lack of maintenance of the building or this one, you have a building that used to be part of the housing stock and you are planning to remove it. And if you do, you need to basically replace it in a timely manner. And if you don't, there are some extra standards you need to comply with. And in this particular case, if we take that particular building that is in such poor condition on the site and apply that standard to lot 6A, then Which is the southern most? The northern one that they're proposing to build immediately. Okay. Then I think we're in very fine shape. If you wanted to take that building and apply it to 6B, then we get to talk about timing and all of those things. So provided that everything still works out for Casey and Ryan as far as their plans to build their home there, timing wise and nothing else going on like another COVID that we would be in a position to be fully compliant with that particular aspect. Okay. Yeah, is there some black letter time limit Marla? So for the housing replacement, it's two years from the date that the zoning permit to demolish the existing house. No, no, for the existing, I get that. I'm talking about the second house. The second house, the housing preservation in theory wouldn't apply because the house that's being torn down has already been replaced. I would just, I mean, my personal view is I would just let it slide. Yeah, I think I included that comment because I knew the timeline for the second house was really soft and I didn't know if you guys were aware of the standard or what the timeline for the first one was but you were telling me that it's pretty immediate. So I don't think this will be a huge deal but I just wanted to flag it as an issue for the conversation. House one's important, house two is not. As far as the standard goes, yeah. Any other comments? John, Quinn? Do you agree? Yeah, I'm good with that, Quinn. Nothing, thanks. Okay, good. All right, so that brings us to the end of the comments. No, one editorial, Marla, you threw me with the double signature. That's not twice. So, keep going. Oh, go back. Oh, you're right, there is, there's this and then there's another comment, okay. So I went through and reviewed the staff report and came to Marty's signature and it's like, okay, that's it. And Casey calls me up and says, what is this last page? And it's like, what are you talking about? Number 14, okay, let me read it. The staff recommends the board discuss the feasibility of this standard. I think it's just the same page twice. One of the same. It's the same comment? It's an additional information that was inserted. Is it, or is it just the same page twice? It's a different comment. No. Yep. Yep, I'm sorry. It's a different comment. To be honest, I actually, this is my first time compiling the packet with Marla out of the office. Okay. So I got a little bit of a- Staff recommends- Now the next question is, does that apply to this application or is that carried over from a previous version that you were modifying? I don't even see the one you're talking about. Let me read it. Let me read it. Staff recommends the board discuss the feasibility of this standard relating to construction, timing and phasing, standard timeline with the applicant and further discuss the possibility in my extended timeline. This seems like it was a previous comment. Yeah. 22 of the PDF. Yeah. I think it's the older version of what became the final version of 14. Easy to do. It was more just to just poke Marty. And what we know is Marty's signature is consistent. So let's turn to public comment. Are there any members of the public who would like to comment? You can use the podium. If you push the button, turn from dull green to bright green. Thank you. My name is Dana DeSano and I am here tonight with my husband, James Rustad and our son. We live at 76 Folcham Hollow Road, the property next door to this lot. And as an initial matter, we want to extend our gratitude for the thoughtfulness and attention to detail by the staff and the board and the applicant as well for this project. Our comment and request has to deal with privacy and landscaping. We live at the bottom of a pretty steep slope. And I understand from reviewing the pictures that there are some large trees that are gonna be removed as part of this. And given that the first floor and the backyard area of the proposed home is gonna be looking into essentially our second floor bedroom areas, it would be our request that there be some sort of landscaping screening at the top of the slope. We're in a difficult position being at the bottom of the slope, putting in a hedge, it's not gonna have that screening effect. So that is our respectful request to the board and the applicant. Okay, thank you. Is that something that you can fold into this? I think it's important for Casey to be able to speak with you as far as neighborly thing. Okay. For the engineers like, oh, what do the regulations say? Do you know Casey? Hi, yes, we are intent would definitely be to put a fence up. I talked with Dave a little bit in the past about what is allowed fence-wise. But we obviously want to have as much privacy as well. So we are definitely on board with discussing options and our plan was to have some sort of privacy fencing put up. All right, so we'll let you guys work it out. So Dana and Casey, we have both of your contact information. If you wanna reach out to Marty, he can kind of put you together because if you guys kind of signed in and then we have Casey's contact information, make that connection. Good, thank you. Thank you. So since this is coming back is there something we should see what they settle on and then work that into the application? There are no standards requiring privacy screening between single family homes to single family home. And I think the grade change here is like a different factor. But generally speaking, like we don't require a single family home to buffer itself from another single family home. They're the same land use. They should be fine next to each other. So the weird grade thing is sort of unique to this two parcels. And therefore I think there is no standard that the DW would regulate this by. The best course of action maybe for the two land owners just to sort it out. Okay. Okay, are there any other public comments? All right, so it sounds like we're headed to continuing this. What would be a date for continuing? I guess that's to you. We've got the first Tuesday in September and we also got two weeks after that, September 16th. Oh, the first week in September works fine. If you had offered something two weeks from now I was like, whoa, there's a lot of coordination to get together with public services staff. We can't do that anyways. So submission revised materials are due two weeks before the next meeting. So we'd need your materials in two weeks, three weeks, because it's a five Tuesday month. So you'd have three weeks to get your stuff. That's manageable. And then the September 6th is a Wednesday. I don't know if that matters to you. Cool. As long as you're here. Okay. So I would entertain a motion to continue this application to hear it again on September 6th, 2023. Thank you, Frank. Any second? Second. Second. Thank you, John. All in favor? Aye. Aye. Carried. Thank you for your time. Thank you, Dave. Okay, I guess we have minutes. Can you push from last time? So I'm going to pressure you to think about it today. All right, minutes of July 20th and July 18th. June 20th. June, sorry, and July 18th. Any changes to the minutes? I wasn't here for July 18th, so I don't know if we can do them separately. I didn't review them or the meeting, so. So do you feel uncomfortable voting for them? I just haven't read them nor was I here. Let's do them separately. June 20th. All in favor of approving the minutes from June 20th? Say aye. Aye. Aye. Opposed? No. July 18th. All in favor? Aye. Say aye. Okay. They're carried. Good. Any other business? Okay, that concludes tonight's meeting and we are now going into deliberative session. So we're going to keep.


Welcome to module 30 of concept topology part 1. Last time we introduced the study of product sets basically and started just the meaning of putting some topology on the product set. I will recall this theorem which we did last time and then we will go ahead. So this was the theorem on xj which is the product of the family x little j's. There is a unique topology satisfying these two conditions. The projection maps pj's are all containers and given any topological space y a function is continuous from y to xj if and only if pj composite f which are so-called coordinate functions of pf they are all continuous for every shape. So this was proved last time and we observed that this proof gives you two descriptions of this topology. Namely you can just say that the topology that we have got here is the smallest topology which is the which all the pj's are continuous or you can just describe it by the sub-base take any opens of set in tau j take pj inverse of that put all such elements in one single collection that will be a sub-base for this topology so it is tau s means what generated by s. So this is another description. So now let us continue the study of the product spaces to some extent whatever we can do in half an hour that is all. Of course the entire course we will keep coming to study of product spaces again and again. So start with a family of topological spaces and take the cartesian coordinate space which we have defined as set of all functions from the indexing set j into the union of xj's with certain property. Let tau be the smallest topology such that all the projection maps are continuous. So this is the theorem that we had. So I can call this as a definition now. Then tau is called the product topology and xj, tau is called the product space of what of the collection tau j or xis or xj's. Whenever we are dealing with a family of topological spaces by the word product space we shall always mean this topology space unless mentioned otherwise. Why I am telling this one because though xis are given there may be many different ways of putting topology on x. When you say product space you should take this that is a convention now just like when we are taking r and then we say usual topology it is a topology induced by the distance function there. So that is a convention. Another important aspect of the product topology is the following. First recall this definition of convergence of sequences in a topological space. What is that? Here any topological space a sequence xn is converges to x that is what it if and only for every neighborhood u of x there exists a case such that n is bigger than equal to k implies xn is inside u. I am just recalling this definition then I am going to use it here now. So a sequence xn inside product space okay. This will convert to x belonging to xj now I am taking the product topology here and the previous definition which we just saw. If and only if each coordinate sequence see evaluate each element at the jth coordinate then you get a sequence x and j right in xj so that must converge to xj. What is xj? xj is the jth coordinate of x okay. So this is one way of more or less characterizing the topology but that is not what we are going to do we are going to only one way characterization is a little more stringent they do not work in complete generality. So if you take the product topology then it has this property is what we are going to see. The necessity of the condition follows from the continuity of projection maps. Once this sequence is convergent pj of that sequence must be convergent because pjs are continuous pj of this sequence is precisely this sequence and where they should convert to pj of x. So that is continuity of pjs will ensure this if this is a convergent sequence then each x and j is a convergent in xj. Converse is what we have to take care of it that is also one line proof. First of all you must observe that for every u containing x something happens that is what we have to verify but it is enough to do it for sub basic open sets. Once you have done it for sub basic open sets finite intersections of that will be verified by taking that corresponding n0 to be maximum of this n1 and n2 in case we have taken. So that will give you the verification for all basic open sets. Once for basic open sets you have to give you have done to each open set and each point belonging to that open set there will be always a basic open set containing of that. So it will come for all the elements. So this is the elaborate way of telling you but we have all seen all these things the role of basis and sub-basis. So here I am going to use it for the first time. So this is the way economically we can do a lot of work that is the whole idea of base and sub-base after all. So let u be a sub-basic open set in xj such that x belongs to u. Then I must find an n, n0 so set for n bigger than n0 all the accents are inside inside what? Inside this open set. So that is what I have to do. Since it is a basic open set that a basic open set u will look like pj inverse of vj for some open set uj in xj for sum j. For sum j that is all right. Now x belongs to pj inverse of uj is the hypothesis because x is inside u, u is this one. So implies that pj of x is inside uj, pj of x is not xj but now convergence of the sequence x and j will tell you that there is an n0 such that all the accents are in pj inverse of uj because all the x and j's are inside uj for n bigger than n0. But that is same thing as again if you take xj is what pj of xn. So xn belongs to pj inverse of uj and that is u. So u is arbitrary open subset, base sub-basic open set we have verified for every sub-basic open set containing the point x. So this is done okay. So let us go ahead with the number of remarks here. In the language of function spaces the Egoterm tells us that product topology is the same as topology of point-wise convergence. If you do not know this terminology from function spaces you are excused from understanding this okay. When you come to that and your analysis teacher says this point-wise convergence then he will say oh this I know that is the other way around it is actually what is happening. Since we have not studied any function space topology yet you may not be able to make much sense out of this remark at this stage okay. So therefore let this remark hang for a while okay. Don't throw it away it will be useful when you study function analysis or any function space topology and so on. In order to facilitate the discussion of relationships between you know x i and x j where i is a subset of j let us introduce okay an important topological concept here. This is just a stop-gap definition but the concept itself will be useful elsewhere also. So I am taking this opportunity to introduce that one here. Start with any two topological spaces okay by an embedding of x and y we mean a function f from x to y such that f from x tau to f is always from x to f x. First part I am taking this subspace fx the subspace topology is tau prime restricted to fx. So this is the notation for subspace topology remember that. So now instead of y comma tau prime I am taking just fx comma tau prime restricted to fx. So this must be a homeomorphism okay. So let me elaborate on this one namely if f is a continuous injection okay first of all why because the same f is there it is a homeomorphism it must be injection and it must be continuous from x to fx from fx to y there is an inclusion map composite with that that is also f because there are two different definitions this is f restriction right. So I am using the same notation f for both of them. So the original f this one is f to fx here and then fx to y inclusion map. So if this is continuous that will be also continuous. So f must be continuous first of all and injective map right. So this must be necessary it may not be an open map may not be a closed map may not be surjective all these things are true when you come down here because it's a homeomorphism if you are here only continuity and injectivity is still there right. So this is what you have chosen. So it may not be an open map or a closed map or may not be a surjective however if you take the codomain of f to be equal to the image of fx with the subspace topology then it satisfies all these conditions that is the definition of an embedding. The simplest example of an embedding is the inclusion map itself from a subspace into the original space. If we identify x with fx via the map f namely x goes to fx then we can think of x as a subspace of y because fx is a subspace of y now fx is replaced by x and so on. Thus an embedding is a direct generalization of the concept of a subspace. You can almost confuse it with a the subspace but don't confuse it because you want to have some separate identity for x. So whenever it is convenient you can identify this x with fx that is the whole idea here because they are after all homeomorphisms homeomorphic to each other. Let me continue with some more remarks given a subset i of j this was my aim of the indexing set. So I am taking a subset of the index inside we can also define xi what is xi product of all xj is j is j is inside i. This is some independent product topology product set and so on. So what is the relation between the xi and xj then there is the obvious projection maps from the largest this one xj to xi what does it do just ignore all the other coordinates. Suppose this is just a only two elements that x1 and x2. So in x1 cross x2 to x1 or x1 cross x2 to x2 you had the projection maps. Similarly what do you do you just drop out one of the coordinates or several of the coordinates retain the rest of them as they are. So this is what is pi is doing here pi of xj retains all the i coordinates inside capital i ignores all of them inside j minus i pi of x equal to xi this is all i because there are no other coordinates here all those coordinates which are here namely i all those j's inside i they are there okay. Once again from the definition of the product topology this topology this product is nothing but the induced topology on xj with respect to the family pj of coordinate projections okay you take the whole space xj but now you take the subspace of all so that will give you this xi it follows from the above lemma that all the pi's are continuous okay no matter which what is capital i okay this i is fixed now this pi is continuous why because the i th coordinate all the j th coordinate of this one is nothing but the old pj so all the j th coordinate j is j inside capital i they are continuous so pi is continuous we shall refer to these maps also as coordinate projections it is like x1 x2 x3 going to x1 x2 okay so we have been using all these things in the case of rn and cn and so on so only those practices we are putting in a general setup that's all okay so we shall refer to these maps also as coordinate projections if k is j minus i that means the left out indices here and let us assume that both i and k are non-empty this is a standing assumption of course it is easily seen that the map pi comma pk from x capital j to xi cross xk this is a homeomorphism this is a one-one map is clear on two is also clear so bijection is obvious here set theoretically why this is continuous look at any coordinate projections here okay they are all the old coordinate one of the pis and pk pk k belong to k so they are continuous if you go from here to this way xj the same coordinate functions will give you that that's also continuous okay so this is a homeomorphism that preserves the projection maps the i th projection here the i th projection here the same thing it is more or less like the identity map okay so this is the way you identify r2 cross r2 with r4 right the beauty of this notation is now it is independent of or independent of the order on the indexing sets therefore i can write xi cross xj or xj cross xi it will be the same xj up to homeomorphism is what we want to say okay in particular for any point y in xk we get fix one point we get an embedding of xi in xj defined by x going to x comma y this x is varying over xi y is fixed which is inside x xk so the whole thing will be in xj so this is just like the example wherein you take x going to x comma 0 or x going to x comma 1 or x going to x comma 1500 or the other way around you can take y going to 0 comma y right so all those are embeddings so that is why the word embedding was defined just before okay these are all embedding so the partial products can always be thought of as subspace is in various ways you may say horizontally and vertically and so on so these these coordinates can be thought of as horizontal and these are vertical and if there are only two of them all right as a further special case of this assume that xj has at least two elements then given any i belonging to j take the singleton i as capital i okay then you have to fix an element y in the rest of them xk then what it will give you it will give you a parallel various embedding parallel embeddings of xi x smaller i right this i inside xj instead of capital i to do a smaller i inside so this is special case which I have already explained with examples alright there is some more interesting things we have to tell you by taking finite intersection of members of a subbase we of course get a base for the topology how does a typical member of this base look like in the case of finite products we know that these are nothing but proto types of rectangular boxes interval cross interval cross interval and so on right right especially when each xj is r however observe that in the case of infinite products at most only finitely many of the coordinates will be restricted what is pj inverse of let us say what is p1 inverse of u1 where u1 is an open subset of x1 it will be just u1 first coordinate cross the entire of xj minus 1 in our notation here okay take k equal to j minus 1 right one particular case here j minus i you have taken i is single point to fix one point there then you have got embeddings now I am looking at inverse mesh so the second coordinate onwards it will be completely free so that it will look like u1 cross the entire of the space built upon j except 1 suppose similarly take u2 u1 now x1 will be free again only u2 will be restricted u2 coordinate will be restricted p2 inverse of u2 will have only u2 restricted all other coordinates are correct therefore the intersection will have only u1 cross u2 and then the rest of the coordinates are all free no conditions there so this is not a box this could be especially when r cross r cross r you are taking all of them are r the other coordinates are freely varying infinitely you know and unbounded right so so this is what you have to be careful here except for finitely many it is fine just like the box but in the case of infinite product at most only finitely many of the coordinates will be restricted in other words if a is a non-empty member of b then pj of a just assume that a is non-empty that is all pj of a okay equal to xj for all but finitely many j belong to j what I am assuming a a is a sub base basic open set okay I am making the comment on basic open sets here in the view of the remark 3 this can be put as follows this I already told you every member of b looks like that means what homomorphic tau u cross xk where k contain inside j is such that i which is j minus k is finite so this is co-finite and u is an open subset of xi because i is finite u itself will look like u1 cross u2 cross uk or again countable union basic open sets only u1 cross u2 cross uk but every member of b looks like that u1 cross u2 cross uk cross the whole of x so coming back to the finite case suppose j is finite the sub base s gives rise to a base b which coincides with the base that we have taken for box topology namely take all u1 cross u2 cross uk okay for instance when j is just two element set you have to note that p1 inverse of u1 intersection p2 inverse of u2 is just u1 cross u2 just intersection which this will says the first coordinate is restricted inside u1 second coordinate is restricted to u2 therefore it is u1 cross u2 however as soon as the indexing set j is infinite the two topologies may be different in any case you may check that the box topology is finer than the product topology this is a handicap in getting continuous functions into the product of xj's infinite products with box topology the if part of the statement two of theorem 2.70 does not hold as seen by the following example see if this where you are given given this one the product topology then we have the criterion number two there a function is continuous if and only if all the coordinate functions pj composite f those are continuous okay so I will show you now an example very easy example which will violate this one in the case of box topology okay so put xn equal to r with the usual topology for all n so I am taking a countable family here okay indexed by n take fn from r to xn to be the function fn of t is n times t okay I think I wanted 1 by n times t here let us see which one will work n times t 1 by n times t is what I wanted then each fn is continuous okay however the function f from r to xn the product space given by ft of n equal to fn of t is not continuous is the claim for instance the set u which is a product of infinite copies of the interval minus 1 plus 1 okay look at the interval minus 1 plus 1 is a neighborhood of f0 in the box topology what I am taking infinite product of minus 1 minus 1 plus 1 is a neighborhood of 0 in every every one so it will be product of it will be neighborhood of the product box topology 000 all coordinates 0 and that is f0 because all the coordinates f of 0 is is n times 0 so it is 0 but for no open interval i around 0 we have f of y is contained inside u can you see that so for that what I needed here was 1 by nt okay t divided by n so what I want to say suppose you suppose you choose a interval to be minus 50 to plus 50 okay then if I take n you have to choose some some n so if you choose say n equal to 500 then that point will come inside here but here I only have an interval minus we have minus 100 to plus 100 or minus 50 okay so f of i is a bounded interval we take some interval okay so I should I should say that given an open interval here okay f of something must be inside u this u is that is a continuity so that is violated this is not true okay okay so an interesting property of the projection maps is that each f pj from xj to x little j is an open mapping it is enough to show that pj of u is open for each basic open set u inside xj okay so here you have to be careful showing only for sub basic is not enough here because you are taking intersections and image of intersections may not be intersection of you have sub basic unions will be okay so sub basic open set if you show that you are done okay you be careful to pj of u where u is a basic open set I should show that it is open inside xj for every j okay so let u equal to intersection of pki inverse of uk i i range from 1 to n this is a typical way as sub basic open set will look like finite intersections of of basic sub basic open sets so this will be basic one set each uk i is non-empty open subset of k xki now what is pj of u pj of u depends upon what j is if j is one of the pki one of the k i is here then pj of u is precisely uk i you remember in the standard notation this will be nothing but uk 1 cross uk 2 cross uk whatever n cross the rest of all other entire spaces xj therefore its jth projection would be just uk i where j is equal to k i i equal to 1 2 3 up to n if j is not equal to any of these first k i coordinates okay n coordinates if one of the other j then it will be just the whole of xj okay in any case in any case they are all open subsets on the right hand side therefore pj is an open map all right all coordinate projections are subjective maps because i am assuming that all the xj's are non-empty that is important here otherwise the product will be empty even though some of the xj's may not be empty even if one of them is empty the product will be empty so you are assuming that then each pj is a subjective map also we have seen that a subjective open continuous map is a quotient map in other words each coordinate space here xj which you begin they are all quotients of the product space okay so this any surjective continuous function then you can give the product you can give the base the quotient topology if you do that first take this xj's take the product and give quotient space you will get back xj the original topology space that is the meaning of this how did you do this just by showing that each projection map is open map okay the same thing applies instead of one single j you can do it for a bunch of j's xj to xi which we have discussed earlier because that is also surjective open map so I want to discuss a few more things here just as in the infinite in the finite case you have x cross x let us consider the case for example all the xj's are x now one single space okay then we have introduced this notation remember that x power i or x power j whatever now I am taking the indexing set as i so its x power i is what is the product over i but all the x i's are equal to x the same topological space same set same topological space okay just like in the infinite case we can define the diagonal set to be all those x i's such that all of them are equal to each other equal to one single x belong to x okay that is the definition of diagonal the map eta from x to this x power i given by eta i of x see when you want to define a map into x power i what you have to do you have to just mention all the coordinates all the all the coordinate functions here eta i of x which you can write eta x i okay that must be x for all i that is the definition of this map eta so this will give you an identification of x with a diagonal by which I mean a homeomorphism or here in the case it's embedding of x inside x power i okay with respect to this embedding you can identify x as if it is the diagonal of okay so I am just giving you more elaborate explanation here eta is injective and it's on to delta x it is continuous because eta i is identity for all i the coordinate projection eta composite p i is eta i this is what I have defined they are all eta i of x is x so they are all continuous so eta is continuous also for any open set u in x okay pi 1 inverse of u is open in x power i okay that is by definition this is a sub basic open set and we check that eta u okay you start with an open set in x but now you can think of x power i to x there is a projection map also now you take the inverse image of that that is an open set but that open set intersection with delta is precisely equal to eta u eta u is delta x intersection minus hence eta u is an open set inside delta x which means eta is an open mapping into delta x so so x to delta x eta is a homeomorphism okay so let us stop here let me just give you one exercise here namely take subsets aj inside xj especially this this exercise is for infinite products okay look at the product set aj if this is like a box the jth coordinate is aj a 1 cross a 2 cross and so but this infinite product i am taking its closure is the same thing as closure of aj's then take the product you know whenever infinite processes are there you have to be careful with the closures right so you better don't believe this one but try to disprove it or try to prove it only after proving it you believe it all right so this is the exercise any doubts okay let us stop here


Everybody for us here rip in 2021 flawless football hobby two bucks full case number 73. It's a tier random team style break You can always find these results at lane sports cards.com. Thanks for joining everybody and good luck. See what we got The whole of Pats play calling thing is A lot of people were saying that bill was calling the wrong place or something like that It's it's like two people call it's it's not it's not it's not going to work Nobody else doesn't leave because it does not work Builds she's a hybrid offensive coordinator like that's another thing is the McGangles loss. That's a very good point D. Woogie or Woogie. I'm not sure how to say your name. Yeah. Yeah. Yeah, I agree Joe judge. Oh that's it. Oh, it's like judge and Patricia together. It's not Anyway guys Yeah Yeah, Vons of Pats and Jagsman is gonna be along your buddy You just got to hope that uh, Lawrence looks good. All right Oh, they're missing this guy right now Super Bowl patch card Patriots James White Fortin Hatch James white nice one there. That's nice three of five dual patch Patrick my home's a second and Josh Allen Chiefs bills look on that Probably is a random right? Let's see where the chiefs at where the chiefs at Michael and and the bills Scott have random at the end You can make this one. Yeah Almost sneak it in a third color for them homes three color for the Allen good stuff, man Arguably two best QBs in the game right now. I don't think there's any doubts Got Texans out of the Sean Watson five of ten Under 26 years old Browns rookie auto Anthony Schwartz numbered four of ten That's sick dirty patch auto Chargers Joey Bosa that thing is filthy. I think it's filthy. Yeah game war That's from 2020 nice Bosa for the Chargers There's green on every part of that card too. Even the yellow has green on it. That's sick. There you go Chargers Tackle the quarterback into the ground wearing that It's a cool one dual patch auto Frank Gore for the nine or 13 to 20 Oh Wait a season for the dolphins anyone to the you My spring board good interbox rookie auto numbered six of 20 Jersey number Devonte Smith You go birds good box so far Hang why there you go man six to 20 on the Jersey number rookie shadows signatures. I believe yeah Nice one Eagles will get that mags James late Sweet feet I'm missing him. Yeah, diamond relic bears Brian Ehrlacher six or seven of ten Sup Randy Sometimes Randy's Orlando magic Avatar shows up.  I'll check personals after this.   Yeah Nice cowboys card there Bears all pro ain't Mike single Terry 9 to 10 one of the goat lion backers Not so good of a coach Rounds Ricky dual patch auto Anthony Schwartz 18 of 20 second Schwartz of the break cowboys greats auto Tony Dorsett 5 of 15 Cowboys are the couple of nice hits Dorsett's got a sick auto honored ink For the Raiders rich Ganon 1 of 10 Raiders rich Ganon Eagles did very well. Look at this signature gloves 18 of 25 Devonte Smith With that green swoosh Green swoosh outline. Yeah birds again. That's hang why congrats again.   Yeah, I think you do have you again. I think you should get a rich game. I don't know Nice chase there and on the back is rookie shadow signatures Jaguars Trevor Lawrence 2 of 10 Sick hit Jaguars. That is awesome. I love the shadow six Braden with the Jags There he is definitely look a lot better week one. I Think he's just gonna keep improving this year. Yeah, nice Lawrence congrats on that The only picky through was like like the end of the game he missed barely missed a couple He missed some but Basically, it's basically like a brand new team. Yes. Yes Coaching stuff. Yeah Yeah, we'll see what he can do I hope for the Jags and for him that he succeeds All right dual relic chiefs bills my homes and Allen three of five good luck on this one nice card a Four two and two whoever's up top after four gets the card one two Three and four that is going to the bills. Congrats bills Again, probably two best quarterbacks currently playing. I Mean not named on ready Quick recap. I don't really don't recap this but I went for a triple patch Cowboys Z deck CD Jumbo patch rookie Colt Sam Ellinger Sweet feed patch for the past James White Raiders auto rich Ganon to 10 Cowboys on a 20-door set to 15 to a patch rookie on a Brown to Anthony Schwartz 18 of 20 Got bears out on Mike Singletary number nine to ten dual patch auto Frank gore nine or 13 to 20 Jumbo patch auto this for 2020 with a gigantic Gigantic grassdain Joey Bosa This game worn rookie auto Anthony Schwartz Browns to 10 and Texas a Sean Watson auto five to ten Ricky jumbo patch to Marche Spengels Sapphire gem Dan Reno 11 to 15 all pro ink paint Manning four of 10 for the Colts. I Sit there got Ruby Jam Kirk Cousins Vikings It's a 20 diamond gem bears our locker seven to ten and a rookie auto Trevor Lawrence shadow signatures to move 10 Big hit for the Jags dual patch once at the Bills in the Mahomes and Allen Shadow signatures rookie six of ten Devonte Smith the Jersey number match there and signature gloves Devonte Smith 18 to 25 That'll do it. Thanks again. Everybody NT is up next


Hey everyone and welcome to Noor's Cove. I'm Yoshida. Today we're going to be doing our weekly budget. I know I'm a little late but I'm just a day late. I try to do it on Mondays. I may move it to Sundays going forward because that's when I really have the time to kind of like do my budget. So anyway, here was last week. I went ahead and did it on my own. We ended up making, I think, oh god, it was $6.50. Okay. Nails, nothing. Noor's Cove, I got a little cheat sheet here. Noor's Cove made $89.42 last week. Now, no. Yeah. Y'all know what? No. Okay. Here's the thing. The money, I made $89.42 but most of it only got a portion of that. So I'm going to put that at $40. Because this week we're getting another deposit. That makes sense. Ms. Elaine, I have $100 down and that is for, I can't remember what it was. I think I took money from somewhere or whatever but let's just do the math here. So we have basically a $6.90 plus that be $790. $790 is what we ended up making. I took $100 off a credit card. I know. Not great but I'm just keeping it real. I'm just out here trying to survive. Okay. The Cardinal got paid. Chase got paid. Uplift, $38.57 got paid. So here I have Capital One. Capital One actually came out this week. City Bank came out. Will come out this week and I gave them $37. HP came out and then I got my booth right paid. Okay. So we're just going to hop in. I didn't even kind of like pre-do it but let's kind of pre-do it here. So I'm just going to use this marker. I got my cheat sheet over here for my A6. Y'all it is to struggle actually. Today I have a job interview for waxing. I've got to just find a way to make some money. So hopefully I can do it part time. So I'll see on the interview what it is that I can actually do what my schedule will be and I'm pretty sure I can work my hair schedule and nail schedule around that. We'll just see. Once I get there we'll see and even if they give me the job. Okay. So first we have hair. I'm projecting it's been a little tight but I'm projecting 650 again. I would love to go back to my 800s and 700s but it is what it is. I have nails to do today but this is like a one of my like not necessarily tests but basically offered a tour for free to like for exposure. So I'm going to put zero but I always say you know you can tip if you like. Next up we have Norris Code. So we know Norris Code this week. I know I transferred about $68 for Norris Code. That went to paying bills and then miscellaneous. I don't think I have anything that I know of. I'll just put zero for now and the total is $718. Let me double check. Trying to math in my head. Always like to brag that I can count money in my head. Yep. $718. Okay. Now let's get to an integrity. I'm going to slide in my little cheat sheet here from my ASIC. So like I was saying capital one I paid last week but it came out this week. So that was due on the first. That was $40 and that got paid. I put gas in here because I bought gas on Saturday I think and it came out yesterday or last night and it was $55. And so normally I wouldn't include it over here in bills but because it's coming out of this money here I had to include it. If you don't understand what I'm saying just let me know and I'll try to break it down for you. Normally it's over here and like cash envelopes or something like that but being that I don't have the money for cash envelopes right now it just came out of my regular money. Citibank. Hopefully that comes out. I made a mistake with the Citibank and let me tell y'all what I did. My Citibank is normally doing the 17th. I like to try to prepay my bills sometimes so I'll go in. So like on Saturday which was the 16th I paid Citibank and Barclays but I normally put in the date that they're due which is the 17th and 18th. Well I forgot to do that with Citibank and I put it down basically for the 16th so I hope it didn't come through last night and then got sent back because I wasn't ready but anyway it's there and then we have Barclays so Barclays was due yesterday so they'll probably come out like the 21st and to get under because the what's the word I'm looking for the interest went over my mouth by 700 something dollars y'all about maybe it hasn't even been a year I finally got that knocked down back to the original amount so I paid that off to $80.11 so now my limit is $2,000 so now I'm back down to $2,000.  I'm going to start with the small things and then I'm going to knock on Barclays and this Chase account and of course contribute back to my house and hopefully I'll have some cash envelopes with that money prayerfully. Okay next up we have Cardnote I totally forgot my Cardnote this is number two is due y'all I don't know what I'm going to do because they basically try to take it out tonight I have no money for that so it'll probably come out in a day or two and then T-Mobile they were to come out on Monday for 247 I just didn't have it so if I'm maybe getting cut off but I'll work something out I always do but that's not getting paid so I can really kind of take it off but it was due this week so I might take it off and then on the 23rd we have booth rents I just like to write it down so that I'll know and you know like here I hope I'm not all over the place but here I put in notes the T-Mobile didn't get paid or it didn't come out and I need money for my Cardnote in my booth rent so those would be the same notes here and the total was $890 the total was $890 I'm going to subtract the T-Mobile from that just put a mark through that because unless unless a miracle happens I'm not paying it let's put 890 71 subtract 247 and at least 643 71 so that's our total 643 71 and I'll fill in these notes sections by myself so if I make $718 that leaves me with $74.29 so I won't quite be in the negative just by taking that out knowing that I didn't pay it knowing that I don't have it you know so yeah so that is it and actually for next week should be the $77.15 from Norris Cove I'll just have to try to remember some of it may come out this week it may come out this week well we'll go over that next week when we do our budget breakdown and review so I'm going to pop these back in and I appreciate you guys patience with me I'm y'all know I don't know if I did mention on here starting the garden so I started the garden and um you know you gotta kind of fight with the garden because you gotta fight boots and all that type of stuff and diseases and whatnot if you want to keep it you know healthy and everything like that so now I've kind of got the hang of that um I can kind of get back to what I love which is planning and making these videos budgeting of course um I just had a sale and I wanted to do this yesterday so that you guys could take advantage of the sale if you were not able to take advantage of the sale let me know because I may extend it um it'll be an automatic discount matter of fact I'm going to extend it for two more days because I go out of town next week so I'm going to extend the sale for two more days just for those who watch YouTube don't follow me on Instagram so you had no clue about um the sale so I'll extend it for two more days so that makes it today and tomorrow this video will be up today so just like two more days maybe three and that way you can take advantage of the sale um so get your budget stickers and things like that you can also get your budget downloads all budget let me state this because it wasn't stated on my site and had to go back in but most of the budget insert most of the budget inserts are digital pretty much all of them are digital so go in there and so there are like maybe two dollars so you can go in there and get your digital downloads for half I mean 40 off it's 40 off so I'm going to again extend that for like two more days for you guys who wasn't able or unaware of the sale also join my mailing list because it did go out on a mailing list so that way that you get it and you're able to take advantage of that as well so if you did order this first go around and you need maybe another two days to kind of look around and want to get some more stuff go ahead stock up because I will be getting rid of a lot of inventory mostly the budget stuff will stay but a lot of things I'm trying to get rid of to make room for stuff for next year and honestly um next year we're going to be heavy on the budget stuff I'm working on a budget um some new budget inserts and things like that and I just can't wait to show it share it with you guys so I gotta get rid of some of the crap that we have but I'm gonna stop rambling and I really do appreciate you guys sticking with me stopping by commenting liking subscribing all that great stuff and I will talk to you guys in my next video bye


This study found that gastric decompression in GD can reduce the risk of postoperative vomiting, POV, and children undergoing strabismus surgery. GD was associated with a lower incidence of POV during the emergence period, as well as in the postanesthetic care unit.