Hello everybody, I am Matthew Miller. I am the Fedora project leader and this is the Fedora council video meeting we try to do these about once a month and We have meetings more often than that usually there on IRC That's internet relay chat for those of you who are not old-school internet hackers It is actually where a lot of Fedora work gets done but we want to also do some of these high bandwidth things and also kind of make what we do more visible to the rest of the world in the community, so we do some video calls And so we have Fedora council people here And we also usually invite somebody to come and talk about something that they're doing in the project or Something that's going on there Think our main agenda then this week is Ifa Maloney is going to be presenting. Did I get your name right there? Is that yeah, okay awesome Presenting on Red Hat's CPE team. That's community platform engineering And then we'll see what other business we have at the end I think maybe we want to talk a little bit about Fedora and coronavirus So that that'll be that'll be an exciting conversation, but we're going to give Ifa the bulk of the time here Those of us who are familiar with Fedora probably know Red Hat puts a big investment in Fedora But there is actually no Fedora team at Red Hat I think pretty much all of us on this call who work for Red Hat work in different groups across the company and I think that's kind of a neat way for a company to invest in an open source project rather than just kind of having a dedicated This is the few people who worry about that and everybody else that you know goes off and does business things We try and have the whole company engaged in parts. That makes sense but the CPE team is actually dedicated towards Fedora and CentOS community needs for infrastructure And Ifa is going to tell us a little bit about how that works and we can ask her questions and we'll You may know her if you've been following mailing lists from weekly announcements about what's going on on the CPE team But we wanted to bring some of that. Like I said to video to make it more visible to people So with that introduction ifo, would you like to go ahead? Thanks, Matthew And thank you for inviting me into this month's call I really appreciate the opportunity to talk to you folks again I have met some of you in Brno in January was able to meet you there And it's great to come back and continue to talk to you about how the CPE team is moving the new way of work a new way of working By still retaining some of our community roots at heart and our community values Um on how we are trying to manage that. I have a couple of notes in an untitled draft. I didn't do a presentation I wasn't sure if it was Presentation slides worthy or not Um, but I am happy to go through my notes with you here today And if you have any questions and feedback for me If you have any ideas of how how we can maybe Build some of the gaps if there is any or if you've any third lady lads. It's going well. We'd love to hear Good or bad. It's all useful So i'm just going to share my screen very quickly And the untitled document is literally the door counsel CPE talking points That sounds great Okay, so can you let me know when you can see my screen? We've got it excellent So the first thing that I've talked to you today about is the work request file policy So we are trialling this policy. It is not it is not On the commandant's list. It is something that we are having a look at and seeing and finding what way works best Some of it will work really good. Some of it won't and we'll have to drop and pivot and readdress But at the moment, um, I have taken some of your feedback from the last time on board I'm trying to figure out a way to get our backlog prioritization more visible It was suggested to me in within the team that your good cells use the tiger board for your project So I've basically copied no point in reinventing the wheel So there I will share this document out with you as well It is in a google doc and I will transcribe it to a hack and defile as well if that's easier for you all to access and both I have Then playing around with this kanban board, which I think I should have it here And here we can see some of our projects in our backlog One of the cells we're looking at and ones that are in progress And the numbers are irrelevant. It is literally just the number in which I put them on the board It is not reflective of their actual backlog priority What is reflective of that is where they're positioned on the board So in progress we have sent us stream the fast replacement and the data center move There are three projects that are in progress Sent us streamers at the moment at the forefront of the team's focus With the fast replacements second to it But not lesser Just hard to get two cards between We also have the data center move, which is also equally as important But it's it's not taking up as many resources as the first two We are also looking at an inbox upgrade for our q2 planning, which I'll speak on in a moment But that directly feeds into the sent us stream And to lesser scent of the faster placement as well In our backlog we have identified the git forage and disk it merged to be the most priority items at the moment And followed by the dnf back in metrics And we have fedora badges in there too We have a couple of other backlog items as well We are the team would like to address the configure configuration management system We have flat pack fedora's Epic brief as well or requirements document knocking around in confluence. I'd like to bring that out a little bit more We have A new tier replacement that we would like to address always gets a fedora. I think has been worked on I just have to update us And the team are also looking at sent us ci and ci cd changelog They're towards the end. They are actually in motion, but they're kind of They're just things that the team are touching base in And actively trying to resolve without it being on fire The idea of this yeah any questions so far I was going to ask what you may be already answering which is kind of what is the size of a card on here like some of these things Seem like there might be be like a one-off project like any Replacement I can kind of see how that would go as basically an epic as a project Whereas sento a stream is basically an entire linux distribution Uh Can you talk to about the granularity here a little bit and how that's decided how that works We actually haven't discussed sizing. Yes. The team are doing sizing We are really in the TV. That's fair. Sorry. I wasn't trying to make a difficult question No, that's okay. I'll answer as best I can and as honestly as And honestly the um the team is very much in the the teething phase of becoming more agile And we do have an agile practitioner on the team that's helping us helping us progress through it We are very much at the beginning phases of it. So everybody is aware of what it is But we're now in the oh, this is what it feels like kind of mode of it and the within these three projects the team have Within these three projects the team are breaking down the tasks in sizes But the actual projects themselves are not translated into any points or sizes yet. They're just projects um This I clicked on so I want to have to change tack a little bit here, but I'll go back The idea of this board here is that when you click on any project that you're interested in it's a view only board But if you see a project that you are interested in or have put forward for work I want to see You know some details about it. You have the project vision You have the platform that it relates to the estimated completion date The tech lead of the project and the product owner and some contact information to reach out as well I would like to add more detail to it because this is really a rough draft of This is what I'm thinking. What do you think? What do I need more of? What do you not want to see here? And and I will note down that t-shirt sizes or points or something to identify the sizing per project is Is needed and that was actually discussed myself and Sarah were just talking about it earlier today She had suggested to break down the sent off streaming phases And I said yes, good idea. Let me see what the feedback is on us So do you think that is something that you would prefer to see on the board? Yeah, I mean it makes it easier for me to understand what's going on when things are, you know, roughly The same size or at least you can kind of see the size of them Especially when there's something so huge as sent to a stream and makes makes it kind of hard to understand It feels like that's going to just sit there at the top of in progress forever Which probably isn't very very useful. So something that can you know, you can see the progression through here Okay, thank you. That's a good point to feed back. I appreciate that The other question I have which I guess kind of turned into a comment as I was thinking about it is I was wondering why this wasn't on the teams dot fedora project dot org taiga But I guess if you have sent to us and fedora stuff together having it in a in a separate place Makes sense If you want to use the fedora one percent of us stuff, I think you're completely welcome We won't we won't mind, but if this is a good place for it That's good too as long as we can make sure we've got good links to it somewhere so people can find it I don't mind either way. I'm more than happy to Happy paste it as much as I will allow me over across to that And I would I just wanted that visual for yourself to understand this is my line of thought and to see if that matches What you would prefer to see Yeah, this is facing backlog. This is super helpful Okay, so yes for the taiga board maybe change the location And yeah, or it makes sure it makes sure it's easier for people to find I don't really care about the url that much I just want to make sure that when people are looking for it It's it, you know, it doesn't feel like it's often somebody's personal project page somewhere that they can't I think the cp item is an entry in fedora doc so we can link it from there. I can help with that. Yeah, okay Yep, sounds good. Okay, and you you can import into the fedora instance from those instances as well I know I had the iot stuff migrated over to save you doing more work copying postings Great, but sounds good. Thank you. Appreciate. I appreciate the help. I'll take you up. I'm at any time Um excellent So great, that's good to hear that. I'm on the right track for visibility purposes with the teams projects I appreciate that I've taken some notes that you've given me and and some Instructive criticism So I'll just jump back to the document today So that covers the work request trial and it is The larger projects that that come into us. We are still looking at how to get the middle pieces We're we're not really any clear on it, but maybe we might just run with a big one and a little one And we'll see where the the little the middle pieces fall Um, I've spoke to you already about the work channels. The project proposals would be super helpful in the epic brief And you can mail it to me. It would be great if you could Bubble that up through I know Marie sent me on one for badges, which is is perfect. Maybe just like Take somebody to filter it up to me. So I have a point of contact. That's consistent I'm more than happy to be that point of contact for you as well so If I think that these documents are probably only accessible to people at red hat Um, and possibly the idea of epic brief is not familiar to people either Um, can you can you talk about a little bit about what an epic brief is and then I can talk a little bit about how we As fedora leadership can get these things to you in the form that you like Yeah, absolutely happy to do that So I might start then with the proposal process and then talk to you about the epic brief that you get to that So the idea behind this is just to get uh one form of communication one one point of contact from incoming work requests to the team so that they're not coming from Six other different places that there's like one source of truth And it's it's not to block out any any ideas or projects that people have It's to centralize them so that we're not losing track of them and things aren't being halved on We would like to do something one thing and do it well as opposed to Five things and half ask them sorry if I'm swearing on But um, this is what we've kind of come up with as a team and we're seeing how it works And as I said earlier, it's all trial basis. We are not putting this in stone We can pivot when we feel we need to and when it's obviously apparent we have to So the proposal would be super helpful if it was filled in an epic brief, which I'll come back to You fill out your details and you send it to me. We then take the proposal and we review That's ambitious, but we will review as we receive and then come back to the requester with some more information We will solicit requirements from them and we will discuss with the tech leads and the cpe management team Have we people to put on this project? What is the technical implementation? What what approach should we take for it? And then based on a scoping from within the team, we would come back to the the experimental cluster with We think we can do if that matches what they would like if that meets their requirements and then start moving the project similarly if something comes in And it's just worth calling out that if we don't have the capacity for We would like to communicate that out equally as well But if we we don't have the people what we don't have the resources We have a reason for you as to why the project can't be done at this time or ever but we would we would like to Take as much work and be as accountable as we possibly can do without turning people out All right The epic brief I mean so just keep going now while I'm on a roll Go ahead. Yeah If you would like to request work You follow that process and you complete this epic brief You need to have a name you need to pop your name on it the date It was submitted and the dependency dates of your project. So if you know that there's It will take the the the fast replacement as an example just if it came out of Nowhere and there's a dependency date on that of november, I believe this year. It has to be done before then So you would have the dependency dates of november 2020 there the summary overview would be that it is a replacement of the current solution That's el in november 2020 because of x y and z What platform does this relate to the door? If it relates to both just take both Is this something new is it an enhancement or replacement? So brand new item an enhancement Not really but it would be a replacement to the current system Is there a workaround in place in the case of us? No, there's not Once that deadline comes We need to have something there and what does it relate to is it's an initiative? This is something new infrastructure are relenged It would be great if you know if we know why it's important to you Why it benefits everybody for doing it? And then what happens if if unfortunately we can't do that And if you have some objectives and goals that you would like your your product proposal to reach Document them And then this may be the most important is that why what does success look like to you? So if you were requesting the replacement to the account system like How would you know if it's done? How would you get that and go? Yep? That's exactly what I want So it's important to really be very very clear as to what's important Why you want something what what it means to you and what does it look like when it's done to you? That's all you need to do for the epic brief stage it comes to me I set some time together in the calendar and we go through the requirements of the project to make it successful We examine what the dependencies are if there's internal dependencies if there's external ones Um, you need to clarify the internal the external whether it's internal to red hat and external as in community Or if it's internal to fedora an external that it could have Have some bearing on sent us infrastructure And a couple of risks if that is our epic brief in a nutshell Okay, um, I'm gonna I try to pull back the red hat curtain a little bit here and it kind of explain how this connects into what happens in Um, the structure for how things get done at red hat and how this relates to fedora as a project um In general in rel development we have things called subsystem teams and those are Responsible for something like you know the compiler team the tools team or networking or virtualization and there's kind of big areas of of the distribution for rel and those each of those teams has something called a product owner and so the product owner is basically What ifa is doing for the cpe team is kind of the team member who's responsible for getting these requirements in and those requirements come from A product manager on the product management side of the organization what red hat calls the business unit and That's where these features and epic briefs come from from a rel platform side obviously Things are a little different in in fedora for one thing. There is no product management For another this isn't quite like a subsystem team and a lot of the things here are infrastructure related rather than being Fedora like distro features that are being developed so Our friend brian exelbeard becks our former fcake is actually now in a role where he is Serving for community projects as kind of the stand-in for a product manager whatever I'm not sure what the actual title is But basically he is kind of in that role So brian is the owner of these feature request these epic briefs from from that perspective so This template is an internal document and I don't know if we If we necessarily need to have that exact thing in in the community I expect that the way that will work is these Things that are epic briefs will come from the fedora council probably mostly from objective leads and and Then we'll work with Fedora council and with you know me marie and people in fedora leadership to make sure that things that red hat can do Are communicated to red hat in in in this format here And I think that will work I don't know it's helpful. I think for people who are working on those things to be aware of what the epic brief Format looks like and what's being asked for but I don't think community members are going to necessarily need to fill out these Exact this exact paperwork in this way because we'll kind of have Some red headers to help work and get that into the right shape Does that make sense ifa to you and does that make sense to everyone else as well? It certainly makes sense to me. Um I like I'm not I don't mind what way you would like to bubble up your priorities and your Your projects to us too that I'm more than happy to work with you and be aware of your own structure This is what we're trying to put around our team to just make it a little bit more easier for us to get through the work Um, but I'm more than happy to if if you prefer a different format Just loop me in so I know where to look for these things and if you could then Use the epic brief for me for the the big ticket items that you really want to push forward That would be really helpful for me because it's in a really clear document that I can Push through to the team and to the cp management and through bex then as well to The father in redhead or elsewhere that would need some extra extra work. It's just putting Documentation in place as a fallback. We have the data. This is what we need I think this makes sense to me. Does anybody else have a comment on this? I mean, we've got a lot of people on the all here And it seems right to me like we would Do the translation of those kinds of requests and fill out the paperwork. I think that's fine I'm just do we have someone from outside of red hat? How does this look to you? I'm not outside of red hat, but I was wondering if we could maybe use taiga for for this epic brief submissions Instead of using a template in a document and then email it to to a one person basically Maybe if if the taiga instance was open for anybody to submit submit ideas That might work better and be more scalable Justin flurry said in the comments that Even if I'm not someone filling out the epics I follow this in the context is helpful And gives a plus one to thinking on feedback curation from the community So one thing we actually have our own fedora council taiga board that ben Runs and I think As i'm thinking about it right now and this is open to change I think maybe the best thing for us to do is to run those community input ideas through there and progress them through that Ben has dropped a link in the chat here. I'm not sure if that will show up in the video Trying to make sure and get that Transcripts it's on the fedora council project on teams for our project org Think if we bubble up our community things through there and then we can what the ones Somewhere on there. There's a phase basically forget this into the cpe template form and we can make sure that that happens I think that will kind of give the cpe team the format they're looking for and kind of you follow the same process as Other internal red hat teams kind of give that interface Yeah, I just put a comment in that if if you're using your taiga board to to capture the Community items that come into you as counsel to action I'm more than happy to have that board bookmarked and keep an eye on it Ping me if you have something gone in there and we can I can work with the council member Or bex or whoever you'd like to direct that request to to transpose that item those items into epic briefs Then for us to follow the formal process that we're putting around our team We're not trying to put that process around you as the community But we would like to follow it for our team for our own clarity and i'm that middle person there that i'm happy to To take the outside and bring it in and then bring the inside back out Awesome. Uh, thank you, ifa. I feel like there should be more appreciation in the world for people who do that being the middle person work because It takes so much effort Oh my god It takes so much effort to do that and it is such a relief when you're working on something To have somebody else say I got this I can I can help me connect those things So, uh, thank you for being one of those those people. That's amazing Happy to help but benefits is all so why not Um, I don't have too much more notes to to get through but if you want to just skim to them super quick Our next quarterly planning for cpe team is 18th of march I forgot the other ones, but I actually think it's on this document here for the q3 q4 dates um, we are looking at the following stakeholders to get some input on Our next on the products that we're next looking toward So as you pointed out Matthew Bex is going is our liaison point person for both business and community at the moment um The cpe management team are also named as stakeholders just so that they can contribute to Capacity of the teams. They know their own staff. They know what they're working on what they want to upskill to and it's valuable for me to know that we have Center CI Project coming up and somebody from the fedora community that works on the cpe team has really expressed a strong want to learn about that So from a management perspective, it's helpful to know that would be a great person to jump on here That's an upskilling opportunity. That's somebody to learn some other skills. So We feel that it's important for them to have that say both for them and their own staff Sarah our agile practitioner is also helping me as well She's great to structure and schedule the the team's capacity for the actual work in progress stuff that The products come in that we can break them down into more granular tasks. She's going to be helping me on my type one too So that would be good and our team leads for technical implementation so they can start thinking about any projects that come in how we are actually going to move that technically speaking And I had put down a note that to make sure to ask for feedback on additional support and fit in the gaps if If we do have any but you've been pretty proactive on that too So I appreciate it. Any other things that we need to consider Yeah, actually, can we talk about the sustaining team and the workflow for that kind of a little bit? Because I don't think that got covered at all. And I think that'll be actually pretty important to a lot of the people listening who Um, we do have a lot of these big epic ideas But also a lot of work in fedora is kind of ongoing smaller things smaller requests Bailey things details um, and I think that's probably actually Uh, not that what we just talked about isn't incredibly important But I think the majority of people's interface with the cpe team will be through that So let's make sure we get that covered. Absolutely. I just wanted to give you some context on this is what we're what we do during these During these quarterly planning, but fair in mind our next one next week is only Jumping away ahead. Okay Go on we'll come back to that. It's a good thing. It's recorded so we can all go back and go. Oh, yeah I saw about there. Um the The quarterly planning is also going to be recorded as well. So I should check. I don't see it being an issue as to why we can't spend it outside as well for more visibility on it But certainly what is discussed and decided upon will be communicated out I have a couple of Details for the column move triple a and then I'll get the sustaining team Column move dates are being finalized with the team today and I'll publish another note on hack and D It'll be linked in the weekly mail Triple eight last let me interrupt and explain that if people haven't been following red hat is moving data centers from phoenix, arizona to I I don't know where somewhere else somewhere in raleigh Washington, okay. Yeah, I'm also rally rdu2 and uh, yeah, so This is very painful for us and we're going to see the pain coming up with some reduced capacity in Fedora infrastructure for a while this move happens But the good news is that we will have More capacity more space better hardware This will be a big improvement. So good and the other thing to note is You know red hat provides that space to fedora and when red hat said we don't have that space anymore It's not like we can say no So, um, this is not on our schedule. This is not something we wanted to do but um We are making the best of it and cp team is making the best of it What what's the main window for the move may I ask? Yeah, sure. We'll start when when's when's the main interruptions going to be essential So we are starting a shipment our shipment out from April 13th. I think that's the monday You shouldn't see too much massive interruption there. Um, the community will have some downtime from Probably from the 6th of April to in around the first remains There's probably going to be a three week window where communities will uh, will Either be offline or will be elsewhere Um, I have a two hour call today with the team to discuss that and see where what we're going to do So that's why I haven't linked anything here to that yet You should have a more a published schedule by the end of the week, but we are very mindful of The door 32 release schedule and we've purposely been structuring the hardware moves to To make sure that there's enough time for consumption and for releases Inner and the the april mark where you'd like to release door 32 so Yep and points out in the comments here that uh, this is actually on the fedora 33 schedule under the infrastructure Um category all a lot of the dates are already planned out here So it's in the schedule map. So if you go to the normal fedora 33 schedule page, you can find these dates here The main ones are communicates from around the 6th of april to the first in may is going to be the problematic and then We're going to be swapping to a slimline version of fedora from may 20th to july 1st So there'll be a six week window where we will have very limited services running through fedora infrastructure We hope that it will be enough time for downloads and And the release timing for fedora 32 between March in those and not mark sorry When are you releasing it? Is it the 28th of april? 21st Somewhere between those two 21st is the preferred target Um, so we've we've had a look and we've allowed about a three to four Four week optimistic three week kind of minimum window um to get the door 32 out and consumed And then we will reduce the service to allow for the larger hardware shipment. That shipment is going from Northern virginia to washington the first bit of the moves that relates to communicates Now that would be the fedora cloud racks and they are being shipped to or do you And and that will be april so april and june are your Do once that you'll find a little bit of less service but then thank you for posting the link in the chat and I said I will have A detailed schedule published on hack and d once it's been finalised with the team And so we're comfortable that we can meet those targets and change them But it's worth pointing out as well that Things happen so dates may change for both the good and the bad and please bear with us while we're Decisive taking this move and let's all say a prayer that it will never happen again But chance to be a finding the permanent they need eternal data center for fedora. Yeah Yeah, we just built our own so the AAA the the fast update is It's still the same good team Can I center up real quick? I want one thing I wanted to point out For the data center move is that you know the attempt is to try and make it as invisible as possible to fedora users So, you know, it'll be mostly affected effecting contributors and just things being slower there But we want to try and make make sure our users still have a good experience In concrete terms fewer builders is going to be a big thing so we'll Probably not to schedule a mastery build while the builders are not available for example But there will be still build capacity and To some degree That is my understanding and also for all architectures peter right if I I Think so There has to there has to be all architectures because otherwise the builders just block them way It's an all or nothing thing So yeah, the people planning this are Infrastructure team members were all familiar with from Long time fedora so confident they've got it I figured as much which is explicitly why I did not ask the question around all architectures Now there will there will be some limitations, but That the core pieces we're going to retain them There was a note sent out a long time ago from Kevin Fensi Who's The main team lead on this work with me and Steven smidgen about what you can expect from the minimum viable fedora Solution that we're going to put in place And what also you cannot expect I'm trying to dig it out of the archive somewhere I will find it eventually and send it on to you, but it's been referenced a dozen times as well Yeah, I remember reading that some time ago I remember reading that some time ago and not being particularly concerned About anything in particular there. So from my point of view it all seems fine And having done data center moves myself before I know how stressful this is Everything's fine And I found the link theater. So I have it popped into the chat for you as well But that's what we're aiming for at Kevin has been actually looking through that and getting a proof of concept together So that's what we're addressing this evening And once we have once we have that nailed down once we have those dates confirmed I was pushed that out into the open put it on a billboard if I can just so people are fully aware So that when that time does come they know We're not all caught in the headlights And the AAA replacement is is going fine There's the team are still working through the two factor authentication with the three IPA API And the fast jason API this week our work is in the public in github the link is there And I will share this document to you. So you have access to all those links And for the main event the sustaining team So come on verna is leading that team and With them have identified the main repos that they are maintaining Here it is Again D. I love this thing So this is what they are looking at and actively going to maintain and this will address the The small fixes upgrades low-level stuff that doesn't require a big epic brief in a process But still needs attention and we would like anything like that to just hit the tickets In in the usual way. We're not changing that process And we are sharing this out just so people are aware that if you're filing issues and bugs and fixes And these are what we're going to be looking at and addressing anything outside of this list may get missed I will happily share this on with you Does that make things a bit clearer to you as The council and the wider community as to how we're addressing that kind of work Yes, and this is the existing um fedora infrastructure and pager Um At relinch cues on pager for making these requests is that There's a lot of trackers here the team follows all of the different trackers or is there one place we should focus things They're trying to and they're still working through it as well The team has really only come together in the last two months And they've spent a great deal of that time identifying the places where people do find issues and bugs and Things and they've made a tracker for the trackers But we are looking to centralize that and make that more clearer And they have also been working on how they would actually like to work again another document, but And the links are there So they've they've decided to have a mission statement And what their day-to-day would look like and this is hugely in Thanks to our agile practitioner who's coaching us in in working in a more in a better way They have organized themselves into two teams One team is going to be purely dealing with the fires that crop up the bugs the unplanned work things that really need a quick fix And team b are going to look at more longer term Underneath the hood that nobody ever sees but you still need it to get the engine running and clearing up the technical debt That the nice stuff that nobody ever sees but still there So Fun team and hard hard work plumbing team that the exactly I hope people get to rotate between teams at Yes, they do. Yeah, that was um that was identified as as a need both for both for their own mental health and um And it's a great off-skilling opportunity Like if you find yourself either joining this team or have been in it in a while Now there's a great opportunity to to learn new things and Meet more people and work with people a little bit more directly than we may have been working in the past So are the Kanban and scrum boards for these teams? Internal or are they public boards? I believe they're public. Um tna the the fire fighting team Have irc meetings and it's listed here. They have a backlog somewhere I'll have to I'll have to tag that in Um, but they review the tickets that are in their board and they assign tickets And they they get working basically and the team be workflow They are still working through it They are going to be a little bit more formal I think they all join the irc meetings and kind of develop what looks like An immediate tna attention and something that can probably go into a little bit of a longer A longer sprint or queue that team be will pick up Yeah Good example is pingos Proof of concepts that would fall into the team be side of things because this is a an idea that they're looking at for longer term benefit I don't know how many people are all familiar with agile terminology by now, but um Kanban basically is a System like these taiga boards we've been looking at where kind of cards Come in on the one side and progress across them and kind of a continuous flow Whereas scrum is the thing you may have heard of with sprints and kind of a I'll kind of focus on start and end ceremonies and kind of The team takes work at the beginning and then from the point of view of stakeholders That's that's the granularity Is is the size of the team scrum and what the team does internally there's their own business So it'll be interesting to see that working on an open source project because You know, it's it tends to be something that works really well on a kind of a tightly knit team working all very closely on the To see in the same same time zone same same work together. So I'm Kind of interested in how This team develops that because it's kind of neat to see agile processes develop as they work in the real world Yeah, and there's every chance that we could end up doing some sort of a weird hybrid called scrumban Yes, right It's totally open. We're we're just going to see what works. See what sticks Yeah, that's cool. And I think that's going to be good for the team and really good for getting a lot of Productivity and reduce burnout and so in that team. So I'm glad to see this Uh, the that so that is the the sustaining teamwork flow and I'll take two seconds of your time and give you back 15 For important council stuff that I'm so sorry. I've spoken to for 40 minutes at the gift forage. Thank you Oh, yes, let's ask about the gift forage. I don't think we need answers here But what are the this obviously was a pretty big discussion on the fedora develop us with a lot of passion We tried to capture that as much as we could and give our community feedback to you What are the next steps there? What are the timelines and who is making what decisions? Um, so as you can see I have four sentences Um, and one of them is thanking you for the contribution. Yes, there was there was loads of of user stories That came in and and requirements and thank you so much for your time in in going through them and pulling them together In in user story format for me that that has been hugely helpful As we stand now, so we send out the requests for requirements Out in externally We've got them and now it's time to bring them back in-house and review the software as a solution offering And also couldn't make to develop out pager a bit more. So we're now in the comparison site stage that is going to be done with the cp management team and the And the tech leads and also I would imagine vex as the liaison person between community and business Um, we're examining what service meets the majority if all of the requirements And then based on scalability and future growth and business continuity both as a community business and as an actual business business Um, to see what makes the needs and what is The best choice for everybody to move toward We are going to be addressing that in the and the quarterly planning next week Okay, and so that's user stories we publish next week or And and so when can we expect outcome from that? Probably at the end of the month. So what we are we next week? Our quarterly planning is the 18th. So I would imagine we would have an output or a decision reached Hopefully by the end of next week, but it may spin into the week after And we we now would have to communicate to all stakeholders who sent in their requirements. This is what we're thinking. What do you think? so it's a lot of I like what you've done here and Readdressed it. There was we compiled 63 user stories in total It was comforting to see that a lot of the the requirements from From sent us from fedora from rel actually overlapped and could be amalgamated into the same user story So that was that was nice to see kind of made A big task a little bit easier Um, but the there was 63 in total usable user stories and I'm going to be publishing them early next week It's not a decision. It just wants you to I just want you to be aware of this is what came back to us and this is what we can run with Okay, thank you Thank you all for your help with it. It's the big Thank you very much for joining us. This was really helpful and useful to me. I hopefully to other people as well Anyone else have more questions for ifa? No, just a big. Thank you. That was very useful Thank you. Don't hesitate to You're very welcome guys don't hesitate to reach out to me I'll pop in my contact details in the chat. I'm either happy to talk learn more work closer with you happy to do that Great. We are very happy to have you in the fedora community working with us on this. Thank you Okay Next topic. Um, I think we need to talk about COVID-19 a little bit and fedora and the coronavirus Obviously Things are escalating everything in massachusetts is closing down including harvard university, which is kind of shocking You know, we don't close for blizzards. So this is A big deal I'm joking a little bit because what can you do? But it's also very serious. You see the news coming out of italy and everywhere else around the world Where I know we've got a lot of fedora contributors that i'm Concerned about the health of and I hope everybody and everybody's family is doing well Um, I just want to talk about you know our events and things and um, you know Block coming up and what what what we as fedora council should be doing and saying about this at this point Then do she give guidance to mindshare about events and what? um All of that I suppose the biggest question I have is When do we have to make a decision about flock or has that already been made? Murray here I'm here. Um, yes We've so we've gotten to a point where we have put a deposit down on an event space um that There's some things in the contract to be able to You know get some or Some of the money back Um, but that deposit the first initial deposit has been made I plan to put this decision or at least get input from red hat And how they want us to proceed with it because they have a lot of people who are focused on events and um evaluating those I don't find myself particularly qualified To make a call like that, especially this far in advance Although I do think that generally red hat is risk averse so The answer might be that it's canceled, but uh, I'm not that's not official news Please please don't take it that way. Um It's still work in progress and the question of when do we need to exactly know by is a good one And I'm going to find out Yeah, um from what I've seen a lot of a lot of you know events around the size of flock are Canceling now and moving to july and august So it is possible, you know It's very hard to predict, especially the future Um, this this could go in a lot of different ways. Um, and it may be that by By august, you know travel restrictions are down, but maybe that they're a lot more severe So I think um Yeah Letting the experts make the call is probably the right thing to do for flocks. So we don't have news yet is right I guess i'm Right now i'm kind of more thinking about like the meet-up some things that we sponsor through mindshare and whether we should Officially put a hold on those Red hat just announced a thing that basically said Uh, if you were having a meet-up above, you know, above 100 people Do not do that if you're having something below 100 people Um, the wording was a little bit different, but it was You should postpone or make that virtual still still pretty strong on those probably not do that Yeah, um, and especially when we're talking about, you know travel outside of your area in particular, um is Strongly Disrecommended that's not the words either, but um, and I think we should probably extend that to fedora events I don't want to flip out, but like I said, you know the news from italy is pretty bad and These are places where there are Any of china as well where they've pretty developed health care systems are having a hard time We have a lot of fedora and a lot of fedora events in areas that are You know, maybe not at that level and are going to probably be hit worse. Um, so You know when we have countries like the u.s. Where we don't You're right. I was gonna say the united states, um May fall under that because we we don't know what I mean. It's a big uncertain thing. So um Yeah, um I I think so I think my thought is we probably shouldn't sponsor any events At least for like the next three months And then I think ascending I think the next question is do we you know fund people to go places I think the answer is also no That's kind of matches what I'm thinking as well. So yeah, I'm plus one to that Um, yeah, I think we can I think we can safely say that for like the next three months And if it's outside of that, I think we can like Look at each case Okay. Yeah, I think we should just do the events that have already been rolling Let's try that one at a time Um, do we have any existing events that are already funded for the next three months? That's a great question. How should we handle that? I'm writing that one down All right. Well the answer is we'll find out I think it makes perfect sense to have a rolling decision on this As things evolve So two questions for me are when do we need to know for flock if we're going to cancel or Keep it kind of a thing or what when would that make sense to make that decision? and Do we have events that are already funded? And we're going to do some rolling decision making on events moving forward Uh, I guess the good news is that people in fedora are well Familiar with collaborating remotely and working from home and using video conferencing to get things done. So Hopefully things will mostly be business as usual for us And hopefully we can you know share some of our expertise in working this way with our other co-workers and people who don't We are doing a good amount of you know, brainstorming around red hat summit So I don't mean we can use some of those same things if we want to do some virtual events It's the same concepts. Um, I think if walk does get canceled and there's a bigger conversation there because that's a huge component for contributors Over the year to kind of give them the energy for the next year. So Right Let's have a conversation when it comes but But yeah, I don't think that just canceling it is The best thing to do. I think we would have to do or I would like to do something I don't think we have to call it like a virtual flock, but I don't know right it's to me To me, um, we do the thing that most people think of as a virtual conference Continually at fedora like fedora is an ongoing virtual conference. That's kind of what we are um So having a virtual flock I mean the whole point of flock is that it is not virtual it gets us together So we can't really have I agree. We can't have a thing that's virtual flock. But on the other hand Doing what we can to do a celebration of the community Even without that seems like a good thing, but you're right. Let's let's wait till it gets to Where we need to do that All right, um, peter you said you had to go halfway through but you're still here. I'm glad we held your attention um Anything else no the the person that I was meeting with cancelled You know, all right Anybody have anything else for the last five minutes of the meeting here? All right Oh good I want to do a quick reminder that um, you know, we're open to suggestion. I just dropped the link in the chat I'll drop it in the council IRC channel. But if there are things that you want to have As part of this monthly video series Add it to the wish list on the wiki so that we can try and get that scheduled Um, I've updated it to include tbd for the next three months, but I already have some ideas in mind I just need to um, you know coordinate with those people and get those on the list Yeah, awesome. And I think technically this worked very well I we've been trained to use jitsi an open source video solution that we are very fond of in theory um, but it was not actually being able to sustain a Whole conversation with all of these people. So Blue jeans it is. Thank you blue jeans.


Hey, Bolo buddies. Thanks for watching. All right. This is one of my favorite Bolo videos because I'm gonna share with you my big money Bolo's and I love every Cha-ching But those big money Bolo Cha-chings are the best I'm gonna tell you where I got it what I paid for it and what it sold for and I think some of these are gonna impress you a little bit because They kind of impressed me. All right. Thanks for being here My name is Courtney and I'm gonna share my Bolo items with you. This is a what sold video.  I went to a garage. So I think I got 32 of these and guess what I Have one left. I actually have two left But I decided to hang on to one my husband and I were talking about it and we're like we should really keep one of those bunnies So I have one left to sell this person bought three of my Birkham bunnies Three of them for a total of two hundred and fifty four dollars and ninety seven cents plus tax and shipping They were all in for three hundred and twelve dollars So let me tell you a little bit about this bunny in case you ever come across them and get so lucky I don't think I sold any of them for under seventy most of them sold for a hundred a piece and I think I paid I Want to say I paid ten dollars for thirty two of them I can't recall but I told the whole story over on primetime treasure hunters thrift a battle between Donna Telebotellino and I So if you want the details go check it out Here is the print and I told the story behind it all of the stuff about the Birkham bunny I had no idea it was gonna be a big money Bolo when I picked this up Here's the other one. This one's blue. Some of them were so pretty these three were just kind of you know more of the plain colors, but Just one of my best finds ever So just just super fun made thousands of dollars on these and I I really didn't know it was a lucky It was a lucky find. I honestly figured I was gonna get these home and I was gonna sit on them forever Now I will say that I have held out for the right buyers and I would not go under seventy dollars and That has made them be some of them a little bit long tail I want to say that was probably a year and a half two years ago when I was on primetime treasure hunters channel, so But most of them sold more quickly these these guys were kind of hanging around which is why I took the 254 97 Alright, so those are the Birkham bunnies Okay now mindful recycle She sent me a box.  I have an unboxing on this channel, but um You guys she sent me a Bolo box. There were so many Bolo items in here.   I wish she put out more content But check her out. You will not be sorry. You're gonna love her channel. Ah Did I forget to pull up the item? Oh, nope. Here it is. I was like, where's the item? So this is one of the items that was in my box and I believe that it would have sold a lot quicker But I had it priced really high because I couldn't find any comps. I had it listed at 150 Had a 25% off sale going on wasn't getting any action Somebody offered me 75 bucks. So I ended up taking that and the buyer was all in for $90 and 95 cents So very cool briar horse. So thank you again, Terry for my Bolo box amazing This right here. I got this at a garage sale for $2. It is a perfume princess and Remember you guys if you are ever shipping perfume, it does have to ship ground This one the box was damaged. It was from 1994. I ended up selling this doll for 48 75 The buyer was all in for $61.94 all in means with tax and shipping the next item just I Surprised myself with this one. I could not find a good comp and A comp is a comparable something like it that was listed that sold. I couldn't find one So I just listed it high I listed this guy at 75 bucks and it ended up selling on best offer for $60. The buyer was all in for 72 30 I got it at a garage sale on a bulk lot of items. I think I even listed this on one of my live shows over on my Bolo Reseller testing Bolo products channel. That's where I do live listings So that's linked down below if you guys want to join over there But I got this for about 50 cents. So how cool is that? Would you have ever guessed? Let me know in the comments. Would you have walked right past it or would you have bought it? The next item are these frogs another item that most of you probably would have been like nope Not listing it. They're damaged. This guy's missing an eye The these are called flocked the flocking flocking I don't know if that's a word but the flocked part is coming off in so many areas. They've got condition issues However, they are vintage. They are the Sylvania and families bull rush frogs They are a harder to find retired set and I got these at an estate sale in a bundle of Calico critter items and I looked them up and I Priced them high because they're hard to find and I sold these guys for $50 the buyer was all in for $58 87 my cost of goods was about a quarter for those The next item is this Paul patrol set. So you guys are gonna love this story Somebody buys it for $45. They ask me to cancel the order. I cancel the order and then I Think I was sending out offers the next day or something like that and the same person bought it for $37 and 50 cents and I'm like what is going on like I Already sold it to you for 45 and you canceled the order and then you buy it for 37 50. Oh Has that ever happened to anyone here? I know a lot of people block buyers when they cancel Do you guys block buyers or I don't typically block them unless I have an issue like if somebody just asked to cancel an order I typically just cancel So I messaged the buyer and I'm like did you buy this by mistake and they're like no I changed my mind and I'm like, okay, so I ended up shipping it out to him I didn't sell it for 45 like I wanted to but that's okay. 37 50 was still great I paid two bucks for this at a garage sale and the buyer was all in for 6190 Which when you add that tax and shipping that adds up. That's a lot of money All right, these Fisher price little people cars These came out of a mystery toy box that I purchased from auctions for you YouTube channel I do have her length as well as Donatella bottolino down below I source from them on YouTube if you're if you've been here on my channel. Wow, you guys know you've seen my unboxings I get some really great stuff, but these ended up selling for a best offer of $38 plus shipping The next item is this pendant I got this at a thrift store for 50 cents and I ended up selling it for $39 the buyer was all in for 47 13 it's vintage signed rainbow gold filled lady angel cameo And you can see right here It's got the writing on it and then it says rainbow gold filled on the back So just a cool little piece. I was able to find a comp on it and I priced it kind of high and it sold really fast The next item is this vintage martha stork cookie cutter this sat in my garage for probably over a year It was in a christmas mystery box from a thrift store. I had No clue that this was a big money bolo This was another item that I really I listed over on my reseller testing bolo products during a live show and you know I'm excited to tell you that I took a best offer of 125 dollars on this martha stort Buy mail copper cookie cutter. It's a jolly snowman and I'm going to say yes It's jolly because 125 bucks in my pocket. Yes All in for 142 on that one These are vintage cards. Um, I think I picked these up at an estate sale or a garage sale I'm not really sure. I was just like a bulk buy But there were some really cute ones in here vintage cards. Sometimes I sell them individually. Usually I just lot them up like this I sold these for 60 plus shipping This big foot.  So I did that but I had to share a bolo and this was the bolo item I picked So if you came over from mountain man treasures video Drop me a comment and let me know that and everybody if you're not following mountain man Treasure definitely go follow him. Troy is fantastic. He has an amazing channel and he just went full time So he is going to be putting out more content And having more items up on ebay. So he is great this big foot I believe it was five dollars at a garage sale And what I said on his video is if you find this item and it doesn't work You can sell just that big foot remote. It will sell you can also sell the charger You can definitely part this guy out. You can even go as far as to Sell the battery compartment cover so Big foot, but I sold this working 150 bucks plus shipping I love that. He is so cool All right Oh, did I miss? Yep. I missed one. No, I didn't Yes, I did Well I missed one. Okay. Sorry about that um, it was a It was a toy. So apparently I didn't pull it up So this is catrin muller mohair jointed bears The same person bought all three of these and if you want to know more about this you can go over to my worth point video that says proof And I tell you why worth point is totally worth it and it has a little something to do with these bears right here So check out that video But this person ended up buying all three of these for a grand total of $325 plus tax and shipping they were all in for 368 69 So I did come down on the price because they were buying all three of them Look, these are not very big. Let me see if I can Here it is that one's only like five inches So I think it was like 70 70 and the bigger one I sold for more That one's about nine inches this guy's bigger But they are just really really cool and collectible, but it did take the right buyer So definitely be on the lookout for those anything like limited edition that is by an artist Definitely look those up So that was a great find. I got those at a thrift store. I believe I have footage and It was a long tail item you guys for sure um But it was at a thrift store and it was not like a goodwill and I negotiated down the price a little bit So I can't remember exactly what I paid for these but I I did end up getting I ended up doing well But I wasn't sure if they were going to be a big money bow low or not until I brought them home and researched I just knew that they were cool Here's another one of those eggs. I talked about these in one of my bread and butter videos So some of these depending on what the print is, but here's what the inside looks like They say Germany. They usually have some sort of print on the inside some are more rare than others This one ended up selling for 45 dollars. I got it at a garage sale for four bucks The buyer was all in for 53 84, but they are paper mache eggs. I definitely recommend you get those if you see them Okay, this one came from auctions for you I bought I want to say It was this set a lego set and a playmobile set And I sold the other lego. I'm sorry. It was a mega blocks. It was a dragon mega blocks I sold it for 99 dollars And I sold this one for a best offer of 265 dollars now I purchased this In well, I didn't know I didn't know if it was going to be complete or incomplete But I knew that either way I could part it out and I did a little search when she was showing it and I looked up that 6762 lego and I was like, oh my gosh, that is a big money bow low I hope it's complete. Well, it was not so I was able to order some pieces replacement pieces off of ebay But unfortunately when I got them the color was not a match. So what I purchased was probably a more modern It was the same part, but probably from a modern set. This is an older set So I was not able to locate the exact things, but I was able to put it together with those blocks And I just disclosed that Let me see if I can show you a picture that they didn't match, but they were there. You see how the they're different colors So I needed more of the brown and I ended up getting this color So I still sold it for 265, but if this would have been complete, oh my goodness And I cannot remember what I paid for those three Those three sets But I think when I broke it down, I had about 40 dollars in this set So that was a great return on my money So you can definitely pick up bow lows on auction sites. This guy came out of a thrift store mystery box It is herb braymire. He is local to this area. He is a Artist he hand carves these and they paint them I think his wife paints them from what I heard and I sold this for 54 dollars and 99 cents plus shipping And I actually sold this to somebody who lived in my town and I actually hand delivered it to him So that was pretty cool and she kind of told me the story behind the item So I got some more information and talked to her for a while. So that was really really cool So I actually just found another one in My garage and I was going through some old stock of totes that I have and I'm like, yes another herb braymire So I was really excited about that Oh, and let me show you here. It's signed on the bottom So whenever you guys see things that are like carved in or this is burned in Just because it's handmade doesn't mean it can't be a bow low. So definitely keep that in mind because it's full card These bubble lights I got at a thrift store. I paid $6 for these and I sold these for a best offer of $95 plus shipping So you plug them in and they bubble These are radco This one right here is an air fixed military figures unbuilt almost complete got this at a garage sale for $3 I sold these for 37 plus shipping The next item is this boat. I got it at a garage sale for a buck because they did not know if it worked I went ahead and posted a video down here in the description that shows how it works And the condition that it's in and I ended up selling that for $48 and 10 cents plus shipping It is a vintage remco radio control speedboat supercharged wildcat for parts or repair So it worked, but I don't it had some issues This is an urtle farm animals horse cow dog figures. They are all marked ERTL, which I guess is pronounced urtle I used to just spell it out, but I was told urtle is the way to say it So I'm going to go with that. So this for $40 and the buyer was all in for $54 $44 I will tell you that a lot of times I part these figures out individually, especially like these bowls and stuff But if I let me see here Right here's my tape measure So that kind of gives you an idea of size But these are definitely something I bow low for for sure The next item here is this vintage brooch. It looks like it has an issue right here But that is just a glare a person actually messaged me and was like, I'm going to have to replace the stone and I'm like, no No, no, no, so you can see right here. It's fine But that's one thing bad about Lighting sometimes it can make things look like it's damaged when it's not So I ended up selling this for $37 plus shipping and the buyer was all in for $45 21 And I got this for a dollar at a garage sale All right, you guys that was 23 Big money bowels. Let me know what you think in the comments.  Do you guys ever feel like that when you get the cha-ching and it's like a A big money item and you're like, I got that for $5 Yeah, it's so exciting. I love love love my job. So let me know in the comments favorite place to source How big is your money pile? Blind is a money mountain Um, and how you found the channel. All right, you guys, thanks for watching


So, in the previous lecture, we talked about connected components and today we are going to introduce a notion of path connectedness which is like more intuitive notion of connectedness. So, let us just see what this is. So, definition. So, this path connected. So, let x be a logical space and we say x is path connected. If for any 2 points x and y in x, there is a continuous map gamma from 0 1 to x such that gamma of 0 is equal to x gamma of 1 is equal to y. So, if we take a picture. So, auto logical space x might be like this x and this y and then there is some gamma which could be very complicated which connects x to y. So, the first thing we want to prove is that first result we want to prove is a path connected space, path connected space is connected. So, being path connected is a stronger notion than being connected. So, proof. So, let us assume that x is path connected, but not connected. Then since it is not connected, we can write x as a disjoint union u disjoint union v where u and v are non-empty open subsets. So, since they are non-empty, let x be a point in u and y be a point in v. So, then as x is path connected, there is a continuous map gamma from 0 1 to x such that gamma of 0 is equal to x and gamma of 1 is equal to y. So, now we simply take. So, the inverse image. So, then 0 1 we can write it as gamma inverse u disjoint union gamma inverse v.  And 0 is in gamma inverse u because gamma of 0 is equal to x which is u and 1 belongs to gamma inverse of v. And both these are open. So, thus we have written 0 1 as a disjoint union of non-empty open subsets. So, they are open because gamma is continuous and therefore the inverse image of an open subset is open. So, this contradicts the connectedness of 0 1. So, a path connected space is connected. So, this completes the proof. So, let us see some examples. So, 0 1 all these nice examples that we know are all path connected. So, I mean, if we take the interval 0 1. So, then any two points a and b, we can join it by a straight line. So, we can define gamma of t is equal to 1 minus t times a plus t times b. So, this is then gamma is a continuous map from 0 1 to this interval 0 1 such that gamma of 0 is equal to a and gamma of 1 is equal to b. So, any two points can be connected by this path. So, the same works for the same gamma works for shows that r and r n are also connected or path connected. So, for r n we can just take two vectors and we can join them by a straight line once again. So, gamma is 0 1 to r n and this is gamma of t is equal to let us say we have two vectors a plus t times b. So, let us look at s 1. So, s 1 is this circle over here. So, once again given any two points let us say this is at an angle theta 1 and let us take another point here which is at an angle theta 2. So, this a and this b. So, then we can connect. So, the point is we can connect using a path which starts at a and goes all the way here right. So, but if you were to write it explicitly so, then we can define gamma of t is equal to e to the power 1 minus t times theta 1 plus t times theta 2. So, we have defined this map gamma t and we need to show that this is continuous. So, we will write it as a composite of two continuous maps right. So, we have this map from 0 1 to r which is t goes to 1 minus t times theta 1 plus t times theta 2 and then we will take the map from r to c which is x goes to e to the power x. So, this map is continuous and therefore, this composite is continuous. So, let us try to see that the spheres ok. So, this is s 1, but how about the spheres right. So, let us just do the example for s 2. So, for s 2 let us say this is the equator this is the north pole. So, let us call it n and this is the south pole this is s. So, if p is any point which is not equal to the south pole then we can what we can do is we can connect we can take this point p we can join the by the straight line right. So, first we consider this path gamma 1 t that is equal to t times n or rather 1 minus t times n plus t times p right, but now the straight line is not going to lie on the sphere. So, p is not equal to s that is important. So, we have to make this lie on the sphere. So, for that note that 0 does not lie on the straight line right the origin. So, maybe I should write 0. So, then this implies that the norm of gamma 1 t is a continuous map from 0 1 to r right and therefore, we can just define this map gamma 1 t by this from 0 1 and the image now will land inside the sphere s 2. So, what is this map? This map is t goes to gamma 1 t divided by norm of gamma 1 t ok. This is continuous. So, this is actually this goes to positive. This is continuous because we are taking a continuous map and dividing it by another continuous map right. So, each of the coordinates of gamma 1. So, if I were to write this as gamma 1 1 t is divided by norm right. Each of these coordinates is a because the denominator is never 0 ok. So, this shows that. So, this shows that n can be connected p using a path. Now, but we want to connect n to s the south pole also. So, for that I mean we can just take two paths this join them. So, we can take this point. So, first we can connect n to this point and then in the same way that we use constructed this path from n to a point p we can construct a path from the south pole to the point p. So, this gives a combined path from the north pole to south right. So, this shows that. So, this shows that s 2 is. So, how to combine two paths is something which we will see precisely in a minute. So, and same proof can be slightly modified. So, a slight modification of this proof also shows that s n right a slight modification shows that s n is path connected for all n gradient. In fact, this proof is better because then we do not have to worry about x goes to e to the power x is continuous right. We can just do away with that ok. So, we have seen some examples of path connected spaces some nice examples where we actually make some pictures and intuitively we imagine ok. So, but now let us continue with our discussion. So, as before ok. So, before we continue like we can also ask ourselves. So, we have seen many spaces so far. So, what about the path connectedness of those. So, let us what the other examples we have seen we have seen g l n r we have seen m n r we have seen the orthogonal groups special orthogonal groups we have seen the unitary matrices s u n right. What about connectedness of these right. So, g l n r let us is not even connected because we have this determinant map from g l n r minus 0 right which is surjective because we can just take minus 1 determinant of this is minus 1 and of course, determinant of the identities plus 1 right. So, therefore, r minus 0 which is disconnected we can write it as u disjoint here in v where u is this half open interval and v is this half open interval right and this is the point 0 which you are missing out. So, when we take. So, the determinant is a surjective map from g l n r to in fact we can just put any lambda over here lambda on 0. So, we get this surjective map. So, this implies that determinant inverse of u disjoint unit determinant inverse of v both are non empty gives. So, we can write g l n r as the disjoint unit of 2 non empty open subsets. So, therefore, g l n r is not connected right. So, but on the other hand we can ask what about g l n r plus this equal to those matrices A in or this is just equal to determinant inverse of matrices with positive determinant. So, we will show that later. So, m n r is just r n square and this is a vector space. So, since r n is path connected that same proof gives that m n r is path connected. Once again the orthogonal groups are not path connected for the same reason because when we take determinant the determinant it lands inside this set plus minus 1 right. And this plus minus 1 is just one disjoint unit minus 1 and once again the determinant is surjective. So, when we take the inverse image of both these open subsets. So, we get that shows that o n is not connected. So, it is important to say that the determinant is surjective because if you look at I mean if you look at g l n r plus. So, let me just write g l n r right. So, when we look at the determinant map at the level of g l n r plus the image lands inside minus infinity comma 0 disjoint unit 0 comma infinity right. But when we take the inverse image of the determinant, determinant inverse of minus infinity comma 0 is empty over here right. So, therefore this does not show that g l n r plus is disconnected. So, what I am trying to emphasize is it is important to say that this map is surjective or at least it meets the components of more than one component of the target space more than one connected component of the target space ok. So, but S o n. So, o n is not path connected is not connected yeah, but S o n is path connected right similarly u n and S u n. So, these are these three examples are very interesting, but they are also difficult to prove and to prove these we need the notion of quotient apology which we will introduce later on in this course. So, we will towards the end of this course we will prove that these three spaces are path connected. And I should say that one should emphasize this result because it is very interesting because S o n I mean is defined as it has a very complicated definition a transpose is equal to identity and determinant of a is equal to 1 right. So, with this complicated definition a priori if one just looks at the definition it is not all clear if it is path connected, but yes we can join any point any two points in S o n with a path which is completely inside S o n ok. So, now let us continue as before an equivalence relation ok. So, this time. So, we define the relation as follows. So, we say that. So, let. So, we define x is equal to y if there is a path from continuous map from 0 1 to x such that gamma of 0 is equal to x and gamma of 1 is equal to y right. So, this is new equivalence relation and let us check that. So, let us check this defines an equivalence relation right. So, we need to check three things. So, first we need to check that x is equal to x right. So, this is easy. So, we just take take the constant path right. So, in other words gamma from 0 1 to x and gamma of t is equal to x for all t right and the constant path is continuous. So, the second is if x is equal to y then y is equal to x right. So, suppose since x is equal to y there is a path gamma such that gamma of 0 is equal to x and gamma of y gamma of 1 is equal to y right. So, then take the take gamma 1 define gamma 1 of t is equal to gamma of 1 minus t right. So, gamma 1 is the composite of 0 1 to 0 1 this is t goes to 1 minus t which is obviously continuous and then here we have gamma right. So, gamma 1 is a path from. So, gamma 1 is a path ok. So, basically what if this is gamma this x this is y. So, gamma is going like this then gamma 1 traces it in the opposite the same path in the opposite direction. So, in particular gamma and gamma 1 have the same image inside x they are this they are different maps from 0 1 to x, but they have the same image ok. And the third thing we need to check is if x is equal to y and y is equal to x then x is equal to z right. So, here we will use a theorem that we learnt sometime back it is about how to check continuity of a map by restricting it to 2 close subsets right. So, let since x is equal to y then x is we have 2 we have path gamma 1 from 0 1 to x a continuous map such that gamma 1 of 0 is equal to x and gamma 1 of 1 is equal to y. And since y is equal to z we have this path gamma 1 sorry this is gamma 2 gamma 2 of 0 is equal to y and gamma 2 of 1 is equal to z right. So, basically this x this y and this z right. So, here we have gamma 1 and here we have gamma 2. So, now we define this map from h ok first we define a map from h 1 0 half x. So, h 1 of t is equal to gamma 1 of 2 t and then we define a map h 2 from half gamma 1 to x by h 2 of t is equal to gamma 1 of 2 t minus gamma 2 sorry of 2 t minus 1 ok. So, let us check that h 1 of 2 t is equal to 1 of half is equal to h 2 of half right. So, this is this is equal. So, h 1 of half is gamma 1 of 1 which is equal to y and h 2 of half is gamma 2 of 0 which is also equal to y right therefore, they are equal right. So, now this what does this mean this means that on the interval 0 1 this half right let us call this set A and let us call this set B. A is the closed interval 0 half and B is the closed interval half 1 right. So, this to x we have defined this map. So, this map is h 1 on this 0 half and it is h 2 on half gamma 1 on B right. So, this defines a map h and this map is I mean this actually defines a map because both h the only point of intersection. So, h 1 is a map on A and h 2 is a map on B and both h 1 and h 2 agree on the intersection in this case the intersection is just the point half right. So, therefore, it defines a map we get a map of sets right now h from 0 1 to x. So, the question is is h continues. So, now recall a theorem right. So, h is continuous. So, since right a comma B contained in 0 1 are closed subsets closed subsets right. So, h from 0 1 to x is continuous if and only if h restricted to a and h is restricted to B are continuous. So, obviously, A and B have the subspace topology right, but h restricted to A is exactly h 1 right and what is h 1 h 1 is h 1 is a composite. So, first we go from 0 half to 0 1 t goes to 2 t right and then we apply gamma 1 to x and gamma 1 is continuous and this map is continuous. So, therefore, their composite is continuous and similarly h restricted to B is equal to h 2. So, what is h 2? First we go from half comma 1 to 0 1 by t goes to 2 t minus 1 and then we compose with gamma 2. So, gamma 2 is continuous this map is continuous the first this t goes to 2 t minus 1 right because we have seen that all polynomials in the coordinates are continuous. So, therefore, this composite is continuous right. So, this implies that h 1 restricted to A and h restricted to A and h restricted to B are continuous this implies that h is continuous right. So, more over h of 0 is equal to. So, h is defined to be h 1 on the interval 0 half right. So, h of 0 is equal to h 1 of 0 which is equal to gamma 1 of 0 which is equal to 0 right and h of 1 is equal to. So, h is defined as h 2 on the interval B. So, it is h 2 of 1 which is equal to gamma 2 of 1 which is equal to z. So, thus h is path from x to z. So, this shows that x is equal to z ok. So, and this also shows if I have topological space x and if I can join 2 points x and y with the path and y and z with the path then I can join x and z with the path which is precisely what we used over here in the example of the sphere. So, we can join the north pole to any point P and we can join the north pole to this point P right and then P we can join to this point S right. So, therefore, we can join the north pole to S. So, this defines an equivalence relation. So, the equivalence classes the path components and similar to the proposition about connected components that we proved last time we have this proposition about path components every path connected subset. So, ok. So, we can write x as a disjoint union of x i's. Now x i's are path components every path connected subspace of x is contained some x i. In fact, it is contained in a unique x i right and 2 every each x i is path connected. So, both these will prove that x i maximal subspaces. So, notice that earlier we had a third point which said that when we looked at the connected components we had that the connected components are also closed. But this is not true for path components ok. So, we will see a counter example in the next lecture. So, remark unlike. So, maybe I should make this in red. So, unlike the connected components which were closed in x the path components need not be closed. So, we will end this lecture here.