Connecting buyers and sellers. That's our job, to connect buyers and sellers. And I feel like what we're doing is we're finding a seller and they're waiting on another agent to find a buyer. Do the deal, get the listing, close it, make 20,000. And that person wasn't buying back into the market. Didn't have to build relationships. I didn't have to build a database. I didn't have to have systems in place where no one ever forgets who I am. The problem is finding the leads and closing and converting. That's why you can't close to a week because you handle actually two deals a week to fill in your lap. Yes. I'm like, real estate crash. They're like, what crash? You know? Because they're thinking prices. We're in a transaction crash. This is just as bad as 2008. It's really worse, honestly. Build your database to the point where you don't have to prospect anymore and buy enough rental properties where you don't have to sell real estate anymore. Bam, bam, bam. Now I have the privilege of introducing our keynote speaker. Ricky Caruth is a real estate broker, coach, investor, father, and husband. And that's with an exclamation point. He travels around the country with his amazing wife and daughter, speaking on the biggest stages about real estate and success. Through his speaking engagements books and YouTube channel, he is on a mission to reduce the failure rate in the real estate industry by bringing awareness that it's not about the deal, it's about the relationship. Ricky has been selling real estate since he was 20 years old, starting his career in 2002. He has been through this roller coaster market and back. After tons of life lessons and ups and downs, Ricky has emerged as the number one agent on the Gulf Coast since 2014. His dedication to his client's hard work ethic, market knowledge, and his key attributes that have placed him a step ahead of the rest. Please join me in welcoming Ricky Caruth. Give it up for her. Ms. Whitley and my beautiful wife, give it up for her too. We travel two to three times a month all over the country speaking to agents, so we got a pretty good life. Thank you guys so much for having me. It's a real honor. I do want to give it up for your local board though. Can we give it up for your local board? I came in for lunch for a second to listen to the economics part of this, but you guys were hungry. I was very eaten. Now, if you never saw me before, which is probably most of you, right? How many people here are following me already? Oh, a lot more than I thought. That's awesome. How many people this is your first time? Okay, good. I like these kind of audiences mixed. So what I normally give is a little bit of motivation, inspiration, education, okay? So it's a little bit of everything. What I want to do is figure out who I'm talking to. That's what I like to do first. So how many people here came because you want to double, triple your business? Oh, okay. How many people came here just to network? How many of you don't even know why you came here? And how many new agents? I'll give it up for the new agents. First words of advice for new agents is never raise your hand or admit or tell anybody that you're a new agent. Let me touch on what I see in the market right now, just in general, like as an industry, and then we'll get into some details and some background and stuff, okay? So number one, just where I feel like we've really went to because of technology, because of MLS, because of how easy things have gotten for agents. I feel like we're in this place and I'm probably more guilty than anyone where we're really only doing half our job. That wasn't a joke. What's our job as an agent? Showing houses, really? That's your job. Connecting buyers and sellers. That's our job, to connect buyers and sellers. And I feel like what we're doing is we're finding a seller and they're waiting on another agent to find a buyer. We have the buyer waiting on another agent to list the property our buyer might want. If you have a buyer, why aren't you going and looking for a seller? If you have the seller, why aren't you going and looking for the buyer? So I feel like we're in this place and I wanna try to maybe help, see, my purpose today is to help move your career into maybe a different direction, but a stronger direction. And I want you guys to really think about a lot of these things, okay, when it comes to being efficient and the fact that you can go as far as you want. This is a complete unlimited abyss. The second thing that I'm realizing right now because of high interest rates are the only people that are buying and selling are people that have to, right? If a seller tells you, I would sell if I could find what I wanted or if interest rates weren't as high or if a buyer is like, you know, these aren't your clients today. And I think what we're doing is we're trying to take every prospect and try to figure out how to handle the objection to the point that they buy today or sell today. You need to start categorizing your prospects better. You need to start thinking about, is this a have to or is this a would if I could client? And the would if you could clients, those are the ones that triple your business in the next three years when the market rebounds. If you have a system to stay in touch with these people forever so they never forget who you are. How many of you have a system in place where everyone you talk to never forgets who you are? Because that's, I mean, it's the glue that holds your business together. It's the only way that you can build a snowball to the point that you make a million dollars a year consistently, you have consistent business. Otherwise, you're just floating in the wind and every time the market shifts, you're just, you're caught. The only people buying and selling right now are people that have to and investors. Investors buying no matter what the market's doing. They buy, they sell, I'm buying every month. I'm selling and buying every month. Investors and people that have to. Now let's wrap our head around how do we capitalize on this opportunity and how do we put ourselves in position to capitalize on the next opportunity which I'm gonna get into. You ready? What's the first word you guys think of when you hear the word Alabama? Redneck. I was in New York and I said that. You know what they said? Mud. You think so? I don't know nothing about mud. Can I see my, where's my slides? Here we go. This is where I live in Alabama. Do you see any mud right there? This is where I was born and raised. How many people knew we had beaches in Alabama like this? Just Google golf shores or Orange Beach, Alabama. A show? Yeah, the Ricky Show. We got beaches. I grew up there, right? And I specialized in these golf front condos. Started in an O2. A lot of people don't realize we have these beaches like a best kept secret when the oil spill hit. You guys remember that? That hit you guys too, right? It was like a little mini recession but BP put out all these commercials. Did they do that for you guys? And it like put us on the map. Every single year our tourism was up, up, up, up, every single year. But this, there it is, that looks completely like, see the little blue building in front? That's all that was there when I started. But I watched all these buildings go up, okay? So let me give you a little background here. I started in real estate in O2. So I grew up roofing houses with my father. That taught me work at it, get up, work all day. Also served tables. I did all kinds of stuff. But I had a football scholarship to Missouri Valley, okay? I'm Marshall, Missouri, N-A-I-A school. I went there for a semester. I came back, I went to Alabama for a semester. I felt a history class. I said, I'm done with college.  So I took my class, and I don't know if I wanna do real estate anymore after that. I get scared you have to death in that thing. Anyway, came back. I was like, I don't know if I wanna be a real estate agent. So I got back on the roof. Roof for how many days you think it took for me to say, okay, I'm gonna be a real estate agent? Three. Let me go take that test. So the day I passed the test, I said, dad, I'm gone, I'm a real estate agent now. Peace. Went to the office full time for 30 days. How many you think I sold? Absolutely nothing. Went back to the roof. I'm like, hey dad, can I get a job? Went back to roofing, did that. I was roofing real estate on the side. Took me eight months to get to my first deal. Then I just started clicking two a month, two a month, two a month. This was 2003. Then the market exploded. A lot like what happened in 2021, but 2021 honestly was worse. It was way stronger market in 2021. But it was very similar. Multiple offers, couldn't have any inventory. Everything was selling like that. And I got caught up in that. I made a million bucks quick. I'm like 25. Started flipping houses, right? Then the market crashed and I just lost everything. And then long story short, I got blood dry until I had to go bankrupt, blah, blah, blah. Guess what? Hey dad, I'm back on the roof. This is 2005. 2007, I got a job on an oil rig working in Mississippi. I did that for a full year every other week. I was like, okay, I can do this for a week and real estate for a week and get back in a real estate like this. Do that for a week, real estate for a week. It didn't work out like that because when you come home from working on an oil rig, you don't feel like doing nothing for about four or five days. It takes you that long to recover. And then I had to go right back. So, but, but, there was this gentleman who was my mentor in the very beginning in Gulf Shores. He taught me everything about looking up property owners, what to say, letters, postcards, listings, like everything. And I remember I was out of the business. I looked at MLS and I realized in 2006, when everybody was getting out of the business and the market was basically done, he sold 30 properties, Gulf Front condos.  People don't need a condo. That's the first thing people let go when things get bad. It's the last thing they go by when things are going good. It's a one-two. This guy sold 30 of them in 2006. So I called him and I was like, hey, Scott, how are you selling all these properties, man? He said, come over to the house. Sit down, I'll show you everything I'm doing. So in the very beginning of my career, what did he teach me? Phone calls, emails, and postcards. I went, sat down with him in 2007. And what did he teach me? Phone calls, emails, and postcards. It wasn't anything different. It was just different messaging behind what we were doing. The messaging then was, hey, you wanna make 100,000, 200,000 today? Now it was, hey, do you wanna buy something for half off? So it was the same thing, just the messaging changed. And that kinda hit me, because it's like, okay, this is just a communication game. It's just about moving your messaging around based on what's happening in the market. Another thing that hit me really hard was, I realized that the people that were buying and selling with me at the top were still buying and selling when I was working on an oil rig and on a roof. But they were using a different agent. They were selling their bad assets and buying good assets. And I was like, man, if I would have maintained the relationship with those people, then I would have made it through the crash. And that's when it hit me that everything that it did up to that point was absolutely wrong and backwards. That's when I realized that the business I was building was for today, not for tomorrow. I wasn't building a career, I was just making money right now. And the reason I say that's because I could find somebody that wanted to make $200,000 today. Do the deal, get the listing, close it, make 20,000. And that person wasn't buying back into the market. They didn't care about staying in touch with me. They took their money and ran. I didn't care about staying in touch with them. I knew they were out. Let me go call 10 more people and make 20 grand. And I just did it over and over and over again. I didn't have to build relationships. I didn't have to build a database. I didn't have to have systems in place where no one to ever talk to, ever forgets who I am. That's the key to this whole thing.    I watched two of them die. Making calls, calling for sale bowners and expires till the day they died. Knowing they were dying, trying to make as much money as they could for the spouse before they died. That's not gonna be me.   You guys realize this? Now you can live off your sphere. If you wanna make a mill, you prospect until you're making a mill. Then you don't have to prospect anymore. You make a mill every year since. How do I know? Cause I did that. You wanna make 500, 200, whatever it is. So I got back in 2008, I'm saying, here, the beaches are just as beautiful. It's 50% off, who wants in? Guess what? You know how easy it was to sell property in 2008? People worry about a crash, like a prices go down. You know how easy it's gonna be to sell real estate? If prices go down, ridiculously easy. And all the agents are gonna leave the business cause they don't know this, even though it should be common sense. They just think, oh God, let me get out of business.  Thanks, mom. So I get back in, I'm selling long story short cause I don't wanna drag this part out. When I get into some meat. By 2014, that was the year I sold 100 properties for the first year. I did that every year since for eight years in a row as a single agent with an assistant. So who was my buyer's agent? Me. Who was my listing agent? Me, I did everything. And don't tell anybody. But 100 properties a year, everybody's like, wow, it's just two deals a week. It doesn't sound glamorous when I say it like that, but it's the truth. Can you handle two deals a week? Could you have the capacity to handle two deals a week? Right, just to process the deals? You know, the problem is finding the leads and closing and converting. That's why you can't close two a week. Could you handle actually two deals a week that fell in your lap? Yes, you could. It's not that hard. So now what do we have? A lead generation conversion problem. If you can handle the two deals a week. How many here want to sell 100 properties a year? Are you all ready? You don't want to. It's too much. Yes, ma'am, you and the pink. 50's good, 20. Towards the end, but you have to visualize how it plays out. At the end, before I got out of production, I was working 15 to 20 hours a week. Because when you build your database up to the point, you're not prospecting anymore. And I built my business on property owners. See, I have this thing. Everyone's making money at six o'clock, seven o'clock at night. Every single agent's making money at six, seven o'clock at night. The question is, are you at home chilling, eating dinner with your family without a worry in the world while eight of your 15 listings are being shown by agents on YouTube? Or are you gonna be the one with the more buyer-based business showing property all hours of the night or having your agents, and now you're managing agents all hours of the night? We all have the choice. We should be thinking leverage. We should be thinking efficiency. How can I have this business, have it all, have a great quality of life? Well, listings is the number one avenue to leveraging. You could, would you rather have 30 active listings or 30 active buyers? Yeah, that's what I thought. So why are we building our businesses doing activities that attract so many buyers and nothing to talk to property owners? It's your choice. You can do it however you wanna do it. Why don't you think efficiency? Having a owner-based business, you represent buyers too. The owners buy, people buy your listings. But guess what? They're high quality and they don't run you all over the place. They want your listing or that's a seller that's buying this over here. They already know. Will you get some buyers that run you all over it? Yeah, but not as much as Facebook ads and YouTube. Should you do those platforms? Should you do social media? Hell yeah. But how should you utilize them to get listings? How do you do that? Remind me in a minute and I'll tell you. All right, where am I? I don't know where I'm at on my slides. Oh, okay. They didn't have to press the button. This is just an MLS printout from 2014 to the end of 2021. The eight years I told you that sold 100 properties a year. This is just straight out of the MLS. That's just proof, right? That I'm not just blowing smoke, okay? Now, the next slide is, it's nothing exact, okay? This is just a visualization, okay? This is 2008 when I got back in the business. You can see the market, prices were still coming down all the way to 2012, okay? If you can maintain, a lot of you guys are worried about, oh, my business is down this year. Who cares? Are you building a career or do you care about 2023? In 2026, are you gonna care what you made in 2023? Or are you gonna be worried about what you're making in 2026? 2026. So why do you care about 2023? Because we're here, that's fine, but are you getting by? Because if you are, great, the market's down 20, 30%. And you're still here.  If your database is expanding during this time, then your business is gonna three, four X as the market rebounds, just like mine did. You can see that I did nothing different from eight, nine, 10, 11, 12, 13, 14. Nothing different in my business. The market did that. And the market's going to re-expand like nothing you have ever seen before this time. Nothing you have ever even imagined is going to happen. So what did I learn in the last crash? I already covered some of this. Number one, closings happen every day forever. Can I get a woo-ha? That was the biggest lesson I learned because I thought my business was correlated to the market. It's not. There's unlimited business all the time. Why? Number one, you can't talk to every single person in your market. True? The process of each deal lead generation to conversion to the actual process of the deal. It jams everything up. Therefore, you can do two a week because you do 30 a week? No. The process compresses what we're able to do. That's why there's so many successful agents out there because there's enough for everyone because you can't, the process is too much. So it creates unlimited business. You can't talk to everyone, the process of the deal and like I said, I'm more career focused, not 2023 focused. So when I think about business being unlimited, I'm thinking about how can I talk to every single person in my market over the course of my career? How can I accumulate the most people to know who I am and never forget me over the course of my career? Cause I'm trying to get to that place. Why don't I have to prospect anymore? And my brand is to the place where two deals a week fall on my lap, but just doing a simple weekly email or something of that nature. If you can visualize these things, you can be in a really good place later. The only thing between you and a million bucks a year are thousands of one-on-one conversations with people in your market. Can y'all hear me back there? All right, in the back. The only question is how long are you gonna drag out these thousands of conversations? For me, let me go ahead and have these thousands of conversations right now over the next couple of years. So I can get to that million, I don't have to prospect anymore, but some of you are dragging this thing out 20 years.  That's fine to have all that. But where is the, at some point, it's gotta be about quantity, right? Quality's great. I'm spending time with my clients, it's awesome. Give them a great experience. But at some point, if your business is gonna be massive, it's gotta be about volume at some point. Volume of people that know who you are. So when's that gonna come into your plan? You feel me? I get excited, because this is life or death for me. This is all I do. I'm a real estate nerd. All right, and relationships over transactions. Okay, that's how I had to realize, wait. If I, instead of just calling people, doing a deal and never talking to them again, what if I made a lifelong relationship with this person and then they do five, six, seven deals and refer me, five, six, seven people who also do five, six, seven deals with me and refer me, five, six, seven deals and the whole thing snowballs into this crazy thing I don't even have any control over anymore and my business just explodes out of nowhere. That's what relationships over transactions do. When I call a prospect, I'm not calling about the property.  Okay, two people. Internet leads, right? Who does that? Okay, well how do you guys get leads? Referrals, Zillow's internet leads. Referrals maintain your business, right? So think about this. That database I was talking about growing up to and then you don't have to prospect anymore and you make that money every year after with that database, that's what referrals are. So when you say referrals, that's telling me that you're just maintaining your business. You're gonna make the same money. You see these agents that make 150 every single year, 250, 350 every year, why can't I grow? We're not doing anything to grow your database, your sphere. You know, you're getting referrals and that's keeping the 150 coming in, the 250 coming in, but you're never gonna get the 300 to 500 to a million doing that and you're in this false sense of security. It's a mirage. It's like, oh, I'm doing deals. You have it, you're just maintaining. You have to grow the database. So when I'm talking to a prospect, I'm not calling about the expires, for example. I know you guys don't call them. Huge mistake, by the way. Two to 18 month old is like butter. It's just like, it's just, it's fire.  Side note, when I'm calling them, I'm not trying to list that property. I'm not like trying to handle objections and get an appointment set so I can show them the best marketing I'm gonna do for them. I'm using the property as an excuse to get into a conversation to see if I connect with this person to see what it is they actually wanna do and why if there's an opportunity that I can help them do it. That's it. Most of my expires that I represented, I represented as buyer agent. Not listing agent because I'm not trying to list the property. I'm just trying to see what they wanna do. And you know what? A lot of them wanted to do, buy something. You know what I wanna say? We decided, we're gonna sell that. You know what I wanna buy this. But I wouldn't even have got there if I would have just been following the script, set the appointment, list that property. So I kind of have a different way of doing it. This is how I treat every single prospect. An online lead inquired about a property. I'm using that as an excuse to just get into a conversation and see what it is they wanna do and why and if I can help them do it. I see you were calling about this property, what's going on? Tell me what's happening in your life. Kids went to college, mom died, got a new job. That's what I need to know. Not when do you wanna see it? I need to know what's going on so I can identify how I can help them. You don't know unless you ask these questions. And so this is the kind of stuff I had to learn because I wasn't doing that before. And until I did this, my business was dead. This is your 2008. What I did in 2008 was I said, okay, time to build a career. What am I gonna do? All right, there's a lot of foreclosures. They're everywhere. Now what do I do? Well, there's like three or four agents that represent all these banks and getting all these foreclosures and making all this money. Everybody was jealous. They were knocking down like 40, 50 Gs a month when we were making nothing and they were just like envy of the town. You guys probably had those here, right? How many people were in the business back then? I said, I wanna be them. So I go try to become an REO agent, start with the BPO's, try to work. Real quickly I realized I don't wanna be a slave. So I said, okay, that's not gonna work. How can I blow this thing up? And then boom, it hit me. Let me go represent the buyers buying these properties at half off in three years when foreclosures go away, prices go up, they resell, buy something else and refer four people to me. Ah, now I can just create one relationship and do like 20 deals over the next five years. And so I was visualizing where the market was going. You see that? I said in three years foreclosures will be gone, prices will rebound, they'll resell, do multiple deals with me and refer everyone to me and my business will blow up. That's what happened right here. That's what happened. I started at an 08, 50% off, come in, let me help you, pa pa pa, and within three years and the next thing you know I'm doing 100 deals a year it's because of what I did at 08. Got it? This is your 08 right now. And the reason I say that's because this is a good illustration of it. The number of transactions were down to 2008 levels. People like, I'm like, on social media, social media, social media is a wild place. When you get like 100,000 subs, the freaks really come out. I'm like, real estate crash. And they're like, what crash? You know? Because they're thinking prices. We're in a transaction crash. This is just as bad as 2008. It's really worse, honestly, when it comes to this. Because the way that it's happening. But you're right in line with 2008 right this second. Now what's gonna happen? We're gonna get back to a healthy five million transactions a year. You can see that's kind of where we were teetering there. 13, 14, 15, all those years right there. Around five million is like a very healthy market.  When we go from 4.3 to five million, does it happen next year? I don't know, it's election year. Anything can happen. Maybe it's the year after. I don't know when things are gonna happen, but I can tell you, they're gonna happen. So we know what's gonna happen. How do we put ourselves in position to take advantage of this resurgence of the market the same way I did the last time this happened? That's what you need to be thinking about. I'm gonna get into it. This market, to me, for one, from 2002 to 2017, when I started coaching and writing and speaking, guess what? I never, not once knew what the 30 year fixed mortgage rate was. 17 was the first year I made a million bucks. I didn't even know the start market crashed in 2008. I can't believe you're saying that for all these people, Ricky. The thing, Alabama talk, the thing about it is the reason I say that is because I want to illustrate the level of focus that I had on one thing, connecting buyers and sellers. That's it. Did I have to know what mortgage rates were to connect buyers and sellers? No, I did not. If they wanted to know, which I got asked twice during that whole thing, and it wasn't even like drilling me. It was just like, hey, do you happen to know what the 30 year fixed? I'm like, mm-mm. I got a mortgage guy. I won't even pay attention to it. Not important, because my job is right here, connecting buyers and sellers. You gotta become great at something, and that's what I became great at, connecting buyers and sellers. So, I say that just to say this. Now, I'm a real estate analyst. I study all the trends in history and all the different graphs and all the different companies and forecasts and everything. And when I look at what's happening right now, guess what? It doesn't remind me of 2008. It reminds me of the late 70s. Right? Was anybody in the business in the late 70s? Okay, I thought I was gonna, I thought for sure I'd get somebody. Yeah? Two? If you were in the business in the late 70s, stand up. Yeah! Yeah! Yeah! Awesome. I wasn't. So you guys tell me if my little evaluation here is wrong, but the way I see it, inflation shot up crazy just like it did in the late 70s. Mortgage rates shot up just like they did recently. 19%. I think it hit at the very top. What did that do? It made sellers who were sitting on 7%, 8% not want to sell. Because they didn't want to sell and buy into an 18%, a 17% mortgage. So guess what? Inventory was low. Guess what? Prices didn't go down. Even though demand got killed by 19%, everybody tries to scare you. Prices ebb and flow every single year. Okay? So were there some micro dips? Yes, there's micro dips and prices constantly and every single year. Major dips is what I'm talking about. Am I right? This is more comparable to then, not 2008, these shifts that happen every 10 years to have different personalities. And this is not a 2008 shift. This is a late 70s shift. But everybody wants to compare it to that because they want to be the next genius that's on the next big short movie. Somebody said, I love that movie. All right. And speaking of the 70s, this is actually from, not CoreLogic, the other one. What's the other? No. Starts with a C. No. I'll think of it in a minute. But this is housing appreciation in the US. Okay, going back to 42. This is national data. Okay? You can see in the mid 40s, there were five years in a row of double digit increases. What did they say back then? It's gonna crash. It's up too high. It's crazy. Never went down. After that, we had a two, a zero, a four, six, a four, 12. Even if you bought at the very peak, you still won. In the late 70s, we had six years where four of those were double digit appreciation years. And this is when mortgage rates went up to 19%. Okay? Did we have a negative year? Not only did we not have a negative year, the next year, 80, we had a 7%, a five, a one, a five, a five, a seven, another 10, another double digit year, eight, a seven, leading up to the early 90s where we did have collectively of 2% down. And look, there were some markets that got hurt in the early 90s. California, you know, everything's local. Okay? So you gotta take a lot of this stuff with a grain of salt. The point is, is that we, this is more comparable to then, not now. If you look at the mid 2000s, you can see what happened there. We're not sitting in that position. 45% of the homes out there own free and clear. 30 plus percent of homes bought right now are cash. All the mortgages, most mortgages, we're at the lowest, people that are late on their payments. Lowest level since the late 70s. That's funny, cause it was a 79, was what we're comparable to when it comes to people that are notice of default, and people that are behind on their mortgage right now. It's ridiculous. This gives you a straight line look at prices. The shaded areas or the recessionary periods. What were you guys doing April 20th, 2020? What y'all, y'all, y'all were just, y'all were working and stuff, right? Well, the rest of the country was shut down, all right? The rest of the country couldn't do anything. While you guys were still going to the park and the movies and like going out to eat. Like no mask, just free ballin'. And you're still here to talk about it. On April 20th, but let's just think though, were you guys a little scared? Right? It was like, is this gonna kill me?  Do I have a job? Does the world exist? We didn't know anything. But I saw that that moment retracted transactions 20%. 20% less transactions through that 45 day economic shutdown, 20% less pending deals. And so that told me, oh Lord, we're about to have this massive rush. We're about to have this massive surge. So I put out a video, it's still there. On April 20th, 2020, that said, when the economy reopens, we're gonna have the largest real estate surge we've ever seen. There were two reasons of it. It was the retraction of transactions that I know builds demand, but also the stimulus that happened. It told me that we were fixing to see some fireworks. Did I think it was gonna last two years? Hell no. No, it's crazy what happened. Later on, let's see. December, I said, we're hit a price bottom. Well, how did I know that? Number one, it always bottoms out December to January. Okay, every year. And then later on in May, I said, not only we're gonna hit positive year over year, we're gonna hit a new all-time high when it comes to prices. This stuff moves in slow motion, guys. The market's not like, you know, gonna turn on a dime tomorrow and everything's different. It's all slow motion, which does what for us as agents. It gives us plenty of time to make our adjustments and absolutely crush it. We know what's gonna happen. We're gonna go back to 5 million transactions. You guys know the inventory story. All through the 80s, we were at 2 to 3 million listings. In the 80s, the 80s, 2 to 3 million. And now we're way under a million in a country with a lot more people, a lot more households. It's crazy. It's insane. If we look at, even if you look at this, look at from, say, 2010-ish or whatever, all the way till now, you see how the graph goes straight up, straight down every year, straight up, straight down? Now that's insane. And even in 2021, the year of the boom, we still had active listings go up. In 2021, the year of the boom, active listings went up in 2021.  Everybody's like, oh my God, inventory. Yeah, it goes up every year and it goes down every year. Nowhere close to where it actually needs to be. Now where's all the inventory gonna come from that's gonna level prices out and maybe even cause prices to go down? Anybody have an answer? Builders? That didn't mean they would keep up in decades. We just gotta build a report out that there were less housing starts in August. Not here, but nationally. Yeah, I saw the report that the young man, he was funny, that the young man had about you guys as a specific area with builders and things of that nature. It ebbs and flows, but it's not enough to keep up, right? The amount of people coming here, I saw the driver's license numbers and all the people coming down. It's still not enough to keep up. So do you think that the amount of building going on will continue and then the amount of demand will go down? See, I believe we're at a place where demand can't go down anymore. We're down to people who have to buy and sell. You can't go any lower than that. Could it go down to 3.9 million or something like that? Sure, it could maybe go a little lower, but we're about there. This is it. And then you got investors. You need to be stacking your investor clients. Every single time you talk to an internet lead or an expired or a for sale buy owner or a geo lead or anybody, at the end of the conversation say this right here. Say, hey, before I let you go, let me ask you something. If I had a great deal on a rental property, would you be interested in that? And then just let them answer and see what they say. This person could be like an active investor looking for cash flow. Oh, really? What do you like? Single family, multifamily, duplex, commercial, what do you, warehouse, what do you like? Stack a list of investor clients. Because like the young man the economist said, well, what did he say about investors? He said, and mind you, he said, I don't know where inventory's gonna come from. First thing he said. But then he said, well, investors could be something if they all decide to sell at the same time. Well, hell, that's gonna be good for us. Especially if you've been stacking a list of investor clients who own all these properties if they all sell at the same time, great. Look at all the listings you just got. It's not gonna be a bad situation. Prices could afford to come down a little bit, right? But prices ebb and flow every single year. You see this? Up, down, up, down, up, down, up, down, up, down, every year. So don't be scared about the headlines and the media and YouTube experts. Like, those guys have been calling for a crash for like, some of them for like three or four years, some of them for like a decade. It's like, if it was up to them, none of us would own a house. We'd just be waiting the whole time. And they're wrong every year, but then they keep putting it out and they keep getting millions of views. And it's like, when are people gonna stop watching these guys? They have a horrible track record. Okay, the current opportunity in Sarasota and Manatee County. We're not gonna leave you guys out. Okay, active listings here, up 25%. Did you guys realize this? This is redfin data. Do you guys feel like active listings are up 25% in the area? How many of you see this as a massive opportunity? How many of you see this as a negative opportunity? How many of you are here? Okay, think about it for a second.  Okay, let's participate. How many of you think that there's an opportunity here, a massive opportunity?  Okay, we're on the same page. How many of you like just NA? All right, so when I look at this, I think, oh my God, I can get listings and then I'm gonna sell tomorrow. Some might, but not all of them will. And now I have an opportunity to build inventory. That's what you need, inventory. Days on the market, right? Up 22% from last year. Things are taking longer on average, or this is median, things are taking longer to sell. So you got more listings, 25% more active listings that are taking longer to sell. I'm like, look at my chops. We don't have this in my market. This is like, this is like the holy grail. This is like the moment. You're in one of the greatest seller markets of all time. And you have the opportunity to build inventory? Who has more than one listing? Who has zero listings? Come on guys, don't be shy. Who has more than one? More than five, more than 10, more than 20? Does he even have 20, 20? Like, Astrid, you know, like, everybody's like, that doesn't count. I'm just kidding. Oh no, yeah, absolutely. Okay, so basically outside of new construction, nobody has more than 20 listings. Dude, okay, can we make a pact? Can we do something? Like, we need to do like a challenge or something. Like, how can I hold you guys accountable? Like, every single person needs to be shooting for, if you don't have 20 listings, you need 20 listings. And you need 30 listings, and you need 40 listings. Would you rather have 30 active listings or 30 active buyers? Okay, so can we put together a plan right now? Can we make a pact? Like, everyone in this room, before the end of the year, have 30 listings. Just go for it. If you get to 21, awesome. Some people looking at me like, oh my God, I can't believe it, 30 listings, I couldn't even imagine that in a million years. And you know what? You're the exact person that won't have 30 listings. Remember, the only thing between you and a million bucks a year are thousands of one-on-one conversations with people in your market. You're gonna drag that out over a couple years, or you're gonna drag it out over 20 years. It's your choice. Okay, here we go. Boom, opportunity, bam. Who's gonna go for 30 listings by the end of the year? Make some noise.  I've been telling you the whole time. You gotta talk to people. That's it. See, we're trying to overcomplicate the process, the business. It's really this simple. Talk to people. Help them buy and sell real estate. That's it. Now, if we have a system in place where they never forget who we are, that's where the magic happens. Again, let's keep it simple. Talk to homeowners. Make a great first impression. What it is that you want to do and why, how can I help you do it? Now or later, and then do a weekly email on the same day of the week forever. So they never forget who you are. It's that easy. I told you, I didn't know what mortgage rates were. I didn't know the start market crash. You know what else I didn't do? All the way till 2017. I wasn't on social. I didn't even have an account. When I started coaching, I had to create a profile. I had a Facebook profile, because everybody did. But it was like my space to me. I was like one of the first ones on my space. I was like, oh, this is cool. And then it went away in a day. And I was like, okay, these social platforms are just here and gone. I'm not even gonna waste my energy there. So I started a Facebook profile, but I never posted or anything there at all for forever. Until 2017, when I was like, oh, okay, I'm gonna do this coaching thing, right? By the way, I wrote two books in 17 and I became the world's first completely free real estate coach. All my services are still completely free. And thanks, mom. And like the guy that brought me up here said, the entire mission is just to reduce the failure rate in the industry. Out of you guys that have been following me for a while, is there anybody here that feel like they wouldn't be in the business anymore if it wasn't for zero to diamond or my content? Oh, really? Can you guys stand up? Like, I just reduced the failure rate in the industry. Give them a hand. One, two, three, four. Wow. See, stuff like that. That's why you do stuff. What was I saying? Okay. Social media. So, you need to be doing social media, but you need to be, now let me come back to using social media to get listings, okay? You ready? All right. What we're doing is we're using social media, YouTube, Instagram, Facebook to try to attract buyers. That's what we're doing, right? Is anybody here getting, you know, focusing on like strategies to try to get listings using social media or is it all buyers? Buyers? Listings? And what's the strategy?  No, it's just. Mm, mm-hmm. Bingo. So, the people that are crushing on our social, guess what? They're not even getting leads from the social. They're getting some leads from the social, but it's a byproduct of what their real motives are to do social. You know what they're doing?  Every agent can put their, put the property on MLS, right? So what are you gonna do differently? Well, I have a platform here where I get 300,000 views a month, and I'm gonna push your property on my platform. It's all geared towards local buyers and sellers. Guess what? You're gonna get the listing. That's one way. Another thing to utilize is pushing your listings on the socials, like making videos of your listings and everything to do exactly what I said in the beginning. Your job. Connecting the buyer and the seller. See, with social, it gives us more platforms to be able to actually do our job. We get a listing, use social to try to find a buyer. What does that do? Get you more listings, because now you use the engagement off those videos as you used to try to get a buyer to sell that listing to get more listings. Plus, the sellers might have seen you on the video and say, oh my God, I like how you advertised that house. I saw that you got 8,000 views. I want you to do that for me. You know, because you did another post. Sold it in one day. Right? So you need, I just want you to think seller oriented with what you're doing on these platforms. If you're buyer heavy, you're creating a business that's gonna drive you crazy. You're gonna have to hire buyer agents. And that might be your thing. Now I know a guy that made 80 that sold about 100 million worth on YouTube, all on YouTube. 98% buyers and he has 20 buyer agents. And he doesn't do production. He just runs it, he does the videos. You know, they have a system and the agents get the leads and they close the deals. Awesome for him. Does anyone here want a team of 20 agents? There might be one or two people here. Like that's your thing. Like you wanna be a team leader and stuff, but not me. I wanna make a meal myself, keep it and buy a ton of rental properties. That's my out. That's everybody's easy out. Rental properties. How many people here own investment properties? Oh, my people. That's how you get to the place where, okay. So think about this. Build your database to the point where you don't have to prospect anymore, buy enough rental properties where you don't have to sell real estate anymore. Bam, bam, bam. Shoot, match, done.  How many people here love selling real estate?  You love it now. You love it now. I said the same thing, but there will come a day where like me, my clients were calling me and I was cringing. Oh, God. I don't wanna talk to this million-dollar listing that's gonna want to make me drive down to the property, do a horse and pony show, dress up, tell them what I think it's worth. There will come a point where you don't enjoy this anymore. You're gonna wish you had to put things in place. Build a massive database, buy rental properties. Got it? The law, okay, that's the short-term opportunity. Right, follow me? So we're all gonna go out and go for 30 listings before the end of the year. What? 20? Now go for 30 and then if you get 20, awesome.  Look, I don't care how you talk to property owners. Me? I know that the only thing between me and a million bucks is a thousand conversations with people in my market. So what am I gonna do? Give me all the phone numbers of all the people in my market, let me get to work. I have no problem going ahead and knocking out these conversations. But a lot of you don't wanna do that. It's fine, everybody, there's a million different ways you can do this, but just stick with me on this for just a second and just think outside the box. Here's the conversation, which is the gatekeeper of all closings. Has anyone ever done a deal without talking to someone? Without talking to him? What's up? I mean, I did one in a thousand. He was overseas, email, electronic signatures at the whole nine yards. I did do one. I was still communicating. Nevertheless, very, very low. So you've got the conversations that's the key to all the closings. 99.99999% of the closings, you gotta talk to them. Then you've got all the activities here of lead gen, social media, Zillow, doorknocking, cold calling, sphere of influence, all those activities of lead gen. Where do they go? All right, back to this same activity of a conversation. Zillow, call them. Facebook, call them. Doorknock, talk to them. Cold call, call them. It all comes right back to doing what? Call them. So I'm like, why am I doing all this when I can just do this and just knock it out? That's my mentality, because I gotta get stuff done right now. I don't wanna drag this out.  I'm ready to get on to the next thing, bigger and better things. I don't wanna drag this out forever. So my thing is, is give me all the phone numbers of all the people in my market. Let me go ahead and get to work. Just move out of my way. I got this. That's me. You can do it however you wanna do it.  You're gonna talk to somebody. So what's the long-term opportunity? So we got the short-term opportunity, stack listings. What's the long-term opportunity? We know we're gonna get back to this healthier market when it comes to the number of transactions. My opinion, what I feel like's gonna happen is that rates will get to a point that entices sellers to sell. Why? Well, how many of you, and you may be somebody yourself, know somebody or maybe it's you, you're in a house, you want to move, but you can't because of interest rates. Only a couple of you know, well, you said you're not cold-collar and talking to sellers, so a lot of you guys probably aren't even, are y'all in the market? Yeah. I'm not even in production anymore and I talk to people all the time that are in a house, they need an extra bedroom, they can't move because they're on a 4% rate, right? Every single day that goes by, they're like, I want to move, but I can't. I want to move, but I can't. I want to move! And they get, this desire to move is building more and more and more every single day. And then more and more people are getting on that train as well. So the number of people who, I don't want to say hate their home because they don't hate it, they bought it, you better like it at some level, right? But they want to move and that demand is building. I think we're sitting on this historic demand when it comes to sellers who want to sell. Now what's gonna happen? They're gonna put their property on the market which adds one for a new listing and one for active listing, right? But then guess what they're gonna do? Take one off the market. So what's that gonna do? Down for active listings. So what's gonna happen in that situation is net even. You got one going on and then you got one coming off net even for active listings. But what happened within that scenario? You had a new listing, so that chart went up for the new listing, you had two transactions, so the transaction chart went up, but active listings stayed the same. Now when this all happens, guess what else we're sitting on? The largest amount of 33-year-olds that we've seen in decades since the baby boomers came through. This is birth rates, 50-year birth rates. You see what happened in 1990? Spike, boop, national association realtor says 33 to 36 is the average average of a first-time home buyer. We have more than we've had in a long, long time. So our first-time home buyer, we don't even know how many first-time home buyers are sitting on the sidelines because they just hadn't said anything. But over the past couple of years, they hadn't been there, but they're there now and they're 33 now. And guess what? Next year they're 34, next year they're 35. There's another group of 33 coming in. And this happens, you see the birth rates for 16, 17 years. And then at that point, they're still 34 and 35 and 36. There's a massive wave of first-time home buyers sitting there. So you've got the trade-up seller making a net even for active listings, but transactions went up. Then you've got the first-time home buyer who takes some property off the market and adds a transaction. So that's a net negative for active listings. So then what do you have? More new listings, you've got less active listings, right? You've got more transactions and then guess what happens to prices?  This is my opinion. And the cool thing is you can bet big on this happening because if it doesn't happen and you worked so hard to go out there and get all these 50 listings, guess what? You still win. But if you can set yourself up for this resurgence of the market to triple, quadruple, 5X, 10X your business and it comes true, guess what? You just hit it. You just made your entire career. This is the average age of the first-time home buyer. These are millennials. There was a survey, 98% of millennials, wanna become homeowners. It's funny cause I keep seeing these charts and surveys saying millennials and Gen Z don't wanna own houses and they'll show the survey and it's like 12% don't wanna own homes. And I'm like, what about the other 88%? Does that mean they do? Yeah, it does mean they do. People wanna own homes, ladies and gentlemen, don't listen to the headlines about this. Okay, so what is all this? Everything I've talked about the whole time I have to do with their business. What? I can't hear y'all, y'all. Shine on high. Opportunity, relationships, call in, conversations. I'll tell you what it has to do with your business. Bring it all together. I'll tell you what it has to do with your business. All the stuff I talked about today. Thank you for whoever clapped once. That was awesome. It don't mean nothing. I don't even pay attention to mortgage rates or transactions or social or any of this stuff. I didn't read headlines. None of that stuff to get to the million dollars. Still don't use social media in my real estate business. You need to, I'm just making a point. The market always surges back 110% of the time every single time. Just look back through history. This thing's gonna come back like a rocket ship. Okay, so here's your daily routine. Ready? Prospect nine to 12.  I know a girl, she gets Facebook Leads. She won't call, call. She gets Facebook Leads and she spends from nine to 12 every day calling the Facebook Leads and she tells me they're horrible. They're fake numbers, they're this, they're that. They're running all over, they're crazy. I'm like, you're spending the time anyway calling. Why aren't you calling property owners? You're spending three hours a day anyway. And it's the same conversation. The Facebook Leads didn't even know you were gonna call or who you are. Your goal every day needs to be to make five new friends or property owners every day. If you do that, 250 working days a year for five years, you got 6,000 friends with property owners in your market that you talked to and created a great first impression followed by a weekly email on the same day that we forever, how big is your business? You're the number one agent in Manatee County. Manatee. You're welcome, Manatee.  Okay, new listings, pending, closed, withdrawn, all of it. Just scan through it, become familiar with it.  Hey, I saw this come up, how you doing? I saw this come up, I thought about you. How's everything going? You'll see properties of an area you're farming, whatever. But you become a market expert literally within a couple of weeks. If you just spend 15 minutes a day just scanning through that. This is your job, to stay on top of the properties coming and going off the market, to understand how to advise your clients on pricing properties, finding them opportunities. This is your job, okay? Okay, so we're gonna make calls all morning and then what are we gonna do all afternoon? Tick tock dances, tick tock dances, okay? Social media is a lot of different things. It's written, it's short form, it's long form video, it's blogs, it's podcasts, it's pictures. There's so many things. Stories, like some people just do stories and they get business. Find, you can't do everything in there. Find your thing within the thing and do the thing. Okay? All right, and then create a weekly email. You guys can actually go to startmyweeklyemail.com and you can see all my weekly emails that I sent out to my clients since last November and just use my templates. This is a screenshot of my weekly email, like data. This was like in May, but it's the same every week. It goes out to 19,000 and then around 7,500 open it up every week. This is just what I've built since 2002 and I close two deals a week off of this. It's all I do for marketing. No social, no call, no checking on people. No, hey, I heard it's your dog's birthday.  I don't do any of that. You should do any of that you want to, not saying not to. I'm just making a point. You go all in on what works for you. This is easy, it's scalable, right? The reason it wins is because I say here's the subject today and here's what I think about it. Here's the stats and here's what I think about it. Here's a great restaurant, here's my experience there. Here's a new development coming in, here's my opinion on it. When you give your opinions, that's when people start listening. Okay, who wants to close one deal a week? All right, let me go back. Let me pick somebody. Volunteer, how many active buyers and sellers are you working with right now? 11, how many deals are you closing per month? Perfect example. How many active buyers and sellers are you working with? Five or six, the most common answer is four. Every time four. Statistically, that's 0.8 deals. Which means if you're working with four active buyers and sellers, guess what? You ain't working on nothing. It's Alabama talking, you know? You ain't working on nothing, okay? This is tried and true over tens of thousands of agents that I've coached. If you want to close one deal a week, you need 15 to 20 active buyers and sellers. That's four deals a month. Gentleman here is working with 11, he's closing two a month, so there we go. Now, who wants to close two a week? That's 100 deals a year. I know you don't, but if you do, and this is what I did for eight years in a row, this is the way I did it and this is the way I teach other agents to do it, because you can calculate exactly how many deals you're gonna do. If you have 25 plus active buyers and sellers at all times, you close two deals a week. It's not a hypothesis. This isn't maybe. This is what happens. If you have five to 10, that's pretty good. Work on them and everything, but realize you need to bump that up a little bit if you want to get here. And then when you get to the place where you don't prospect anymore, you're gonna close 1% of your database. So like I've got the 19,000. Then when I quit selling, I had 10,000. When I quit prospecting, I had 10,000. I was closing 100 deals a year and I continued to sell. I quit prospecting in 2017 and I continued to sell 100, 18, 19, 20, and 21. And then I got out of production last year. My dad handles all the day to day now, so I can do this.  So if you wanna close 50 deals a year, build it up to 5,000 and call it a day. You wanna sell 100 a year, bump it up to 10,000, call it a day. Now how quick are you gonna get there?  If you make five new friends or property owners every day and do that 250 working days a year for five years, you got 6,000 right there. You could cut it off right there and do 60 deals a year for the rest of your life. No prospecting. Weekly email. Text me. All my free training, scripts, templates, all that stuff. Happy to connect with you guys. I'm not done. I got one more thing. Unless you're just clapping for the free coaching and stuff, that's cool. All right. You master it? Yes, ma'am. It's vibrating. I'm good. All right. You guys remember that stat that was going around about the, this was in 2021, I think it was. There was like this stat. I never did really find it, but it was like a slide and it said that 8% of the entire real estate agent, the realtor population, had sold four properties or more. 8% had sold four properties or more. Do you guys remember that stat? Did you see it? It kind of like went around. I saw that number four and I thought, okay, something's there because, remember the most common answer of people that have active buyers and sellers was four. Like every time it never fails, four, four, four. And so I was like, something's with this four thing. And then, when it really hit me, was that no matter how big of a group I talked to, I'll give a challenge. Like for example, go get 30 listings before the end of the year, okay? And guess what? I don't care if I talk to four or 5,000 people or a hundred people. Guess how many later on actually went for it and tried to accomplish that goal? Boop. So what I wanna know is, as soon as the four people in this room, that's actually gonna go out there and try to get 30 listings before the end of the year. Make some noise. There can only be four of you guys. Now at the end of the day, I'll wrap it up with this. Your 2024 has already started. You guys know that, right? It's a three month lag business. So if you want to crush 2024, that means what? You need 12 months worth of production, okay? So if you need 12 months worth of production, why do we all wait till January 1st when it's a three month lag business to try to get into action to hurry up and have a great 2024? It doesn't make any sense. The 2024 starts, it's already started, right? August 1st is when your 2024 started. What you're doing now, planting the seeds, meeting new people, they're gonna do business with you next year. Even listings you get right now, probably aren't even gonna close till after the first of the year, you know? Maybe, it's probably a 50-50 shot. It's getting closer and closer every day.  Let's go crush it, right? I'm gonna take a couple of questions. You guys make some noise, thank you. I'm gonna take a couple of questions. You guys have any? What's up? No time for questions. Maybe one question. Yo, you can text me there. Everything's right there, zero to diamond.com or my Instagram. Thank you guys.


Hello, welcome to NPTEL NOC, an introductory course on point sector power here, part 2. I am Anand Arshastri, retired emeritus fellow from IIT Bombay Department of Mathematics. I have a team of teaching assistants here, Professor Ankum Tikken Singh from Nehru in Shilong, Professor Arjala and Bhopang also from Nehru Shilong, Oankar Javedkar from IIT Bombay and Sushil Singla from Shivanadar University. So as name suggests, this is the part 2 of the point sector power here, point sector power here, part 1 was also a NPTEL NOC course which was introduced in the last semester. You can have a look at the content page here, bibliography and content page, chapter 1 on differential calculus on Banach spaces, then compactness and separation axioms, there are compactness and partition affinity, other notions of compactness, compactification, metrization, nets and filters and global separation axioms and then Hurwitz-Walman dimension theory and one more chapter named it is not shown here unfortunately. Very important chapter manifolds. So the point is that the second part naturally assumes that the participants of this course are fairly familiar with the content of part 1. We actually do not assume that you have attended part 1, you may have learnt that part on your own somewhere else from through books or some other course but if you have attended part 1 lecture and have understood a good percentage of that material then sailing with this part 2 will be very easy for you. So such people will benefit much better than people who have not attended part 1. The course is delivered in 60 modules of approximately 30 minutes age just like many other NPTEL courses. We expect that learners will be able to cope up with 5 such modules per week that is like a 2 and half hours contact hour. An important aspect of mathematical studies is to keep a continuity. If you do leave something out somewhere in between it is most likely that you will have difficulty in understanding from later chapters, later portions. It can happen immediately also or it may happen little later also. Quite often it happens immediately so that is what mathematics is. So the key here is keep the continuity, continuity of studies. In any case you have your YouTube, you are free to use them in your own free time so that is the whole advantage of having these recorded lectures. In order to have the students in this respect, in this respect means work in keeping touch with the whole thing. We have a discussion portal in which all participants can raise their queries. Suppose you have not understood something despite having tried. You can try to get these difficulties squared by the team of these TAs. So they are quite enthusiastic, enthusiastic about teaching. They will be constantly looking into these queries. The common portal is there for all of you to put your questions and then they will be responding to them also. The set of lecture notes for part 1 as well as for part 2 will be made available right in the beginning of the course. So that will also help you to understand the material. Along with this, there are also a number of pre-planned live interactive sessions directly with me. With more enthusiasm from the participants from your side, additional interactive sessions can be arranged that is courtesy NPTEL team of course. Let me give you a little elaborate description of the course details. We come to the old spirit namely part 1 whatever we started with, namely what to impact the basic topological ideas and training which will be very useful to people who may not want to study topology itself later but may want to do other subjects also like differential topology, differential geometry, algebraic topology. These are directly topological areas whereas lot of topology is used elsewhere like first of all in analysis for example. Nowadays topology is used by physicists also. A cursory glance at the content which I have shown earlier should confirm this claim. So the entire course along with part 1 and part 2 will not take you much deeper in any particular aspect but it will give you a wider and more fundamental you know training that is the whole idea. Apart from covering all standard topics in topology at this level I mean we have also covered some material which is not available in standard textbooks. The entire course is divided into 12 chapters varying length of course okay not exactly this much portion and so on. Depending on a certain thematic cohesiveness we have classified them chapterized that is all. In finally many chapters many ideas intermingle they are not completely independent after all the entire mathematics is cohesive work. In the first introductory chapter just like in part 1 we discussed something about Rn okay and this time little more namely Banach spaces. So we discussed differential calculus on Banach spaces. This is not a standard topic in topology nor it can be found in elementary differential calculus. Usually it is included or covered in some advanced analysis books. Since this result uses a little more topology which we have already developed in part 1 we feel that we have chosen the right place for it here. Chapter 2 is about compactness and separation axioms and heavily depends upon materials that we have covered in part 1 that is the whole idea of giving you at least the notes of part 1 also. We mix compactness and house darkness which form a central concept these two are central concepts in all topological discussions. Apart from that we have introduced some new concepts such as locally compactness as well as compactly generated spaces. Chapter 3 is devoted to study of veracompactness and partition affinity which is one of the very very powerful tool in topology. In chapter 4 we introduced various notions of compactness such as sequential compactness, countable compactness etc. and their interrelationships especially for metric spaces. We also discussed characterization of compact subsets of a complete metric space in terms of totally boundedness something like what we have done Hannibal theorem and so on. Finally we present the well-known Ascoli's theorem which deal with Bolzano-Oestras property in function spaces you know real valued or complex valued function spaces which are very very important in analysis particularly. In chapter 5 we discussed compactification in general and then two specific ones namely one is called Alexander's compactification or one-point compactification the other one is Stonetsch's compactification. Discussion on related concept to one-point compactification namely the concept of proper maps is included. We then move on to the full discussion of Ston-Weistras theorem. Ston is common here. Ston is a Ston-Weistras theorem they are different of course. The Ston-Weistras theorem you must be knowing that it is about approximating continuous functions by polynomials that is the standard Weistras theorem that will be widely generalized by Ston. In chapter 6 we present Eurydor's matrization theorem and Nagata-Smirnov matrization theorem two of the important ones there are many other versions which we cannot cover. So these things brings out the close relationship with metric spaces and para-compactness especially the Nagata-Smirnov. In chapter 7 we study the concept of nets and filters. Each of them is a vast generalization of the concept of sequences. These are devices invented to do the job of sequences in the absence of a metric. There are several interesting follow-ups of the study. Among them an easy proof of Tyknoff's theorem is work mentioning. Of course we will cover that. Also with the help of filters we could then discuss another important compactification. This is the third one namely due to Wallmann. This is called Wallmann compactification. The other ones were Alexandrov and Stoncheck. In chapter 8 we introduce another not so standard topic namely global separation properties as compared to the local separation you know horse dorseness, regularity, normality and so on. The three separation axioms horse dorseness, regularity, normality are essentially local in nature. So in this chapter we introduce certain global versions of them. They are very close to them but they are stronger than that stronger than local version which is just a step first step towards the general theme of globalization that has to come in the next chapter namely dimension theory. So this is like a precursor preparation for the next chapter dimension theory. Essentially we are giving a detailed account of the concept of zero dimensionality without introducing the term dimensionality you know that is hidden here but this chapter is as as I told you it is a precursor to the next chapter which is about the dimension theory. So I am closely following the book of this Khuravish and Wallmann for this chapter and the next one. In chapter 9 we introduce the study of topological dimension theory due to Khuravish and Wallmann. Our aim here is a modest one for instance we shall prove that the topological dimension of every non-empty open set in Rn is equal to n for deeper aspects of this theory as well as comparison with other dimension theories such as there are many other dimension theories such as Lebesgue covering dimension the reader may look into the book of Khuravish and Wallmann okay we are only covering a very little amount of the material covered in this book. Chapter 10 is devoted to the study of order topology and the space of ordinals with a view to introduce a number of counter examples in an economical way. On the way we discuss some basic set theory such as well ordering and the principle of trans-finite induction just as a matter of you know recalling for ready reference we are not going to teach you the elementary set logic okay logical aspect of the set theory that we are not going to okay so these things are useful everywhere in higher mathematics so we just recall them also here after that we go to order topology and that is our motivation is to introduce a lot of interesting counter examples. In chapter 11 we discuss the problem of putting topologies on function spaces and discuss the compact open topology in some detail. We then present two applications of this the first one is a result due to Michael on quotient spaces quotient maps in the second one we discuss the question whether the group of homeomorphisms of a space forms a topological group under the compact open topology or not so this part is based on a talk I gave on this topic in a meeting at ISI Kolkata in 2019 to celebrate 60th birthday of our close friend Parameshwaran Shankaran from IMSC. In the last chapter number 12 we come to the study of central objects in topology namely manifolds after laying down some foundational results on general topological aspects of manifolds we devote some time in complete classification of one-dimensional manifolds and the last part is a sketch of the classification of two-dimensional compact manifolds so especially this part though it comes at the end we would like to make it a joyful experience like playing with you know piece of paper and so on okay you might have heard about Mobius band and such an important aspect of the course is the set of time bound assignment released each week they are not only meant for 30 percent of the total marks you know 30 percent 70 percent meant for final exam 30 percent is meant for these assignments but these assignments they are essential part of the course imparting problem solving skill they range from quite easy to sufficiently hard of course they will depend on the portions covered in the course up to that point see they are weekly assignment so end of first week you will get some assignment based on the first week things or maybe something calling part one that that's the kind of arrangement is there okay learning the correct solutions through interaction even after submission will greatly help in solving subsequent assignment as well as in the final exam okay so take care of that just because you have submitted these maybe it's wrong maybe it's not wrong the learning process is not over it's only beginning okay here is a list of references some of them are listed because I have borrowed material from them some of them are there because as a student I got familiar with them and liked them and like them even today some of them are there because I would like you to look into them for your further study some of them I might not have studied myself for the course itself you need not look anywhere else I am going to give you full notes as I declared so here are the references Armstrong's basic topology is a very popular book Lagundu G is topology that's the universal book this is the book many of generation you know topology is from our generation learnt topology from this very respected book okay so Douglas Harris this is a paper Khorevij Malman two or three chapters fully I am referring to that book this is my ex-kali's very nicely written book like a this is like a guide to another important book Kelly Kelly's general topology from which I learnt my own topology as that so there is another paper here then Michael's paper Milner's paper and this is Booh emergence of this also another paper Booh Christ topology is also very popular this book I found it very nice foundations of topology by Vainay Patti so he for example covers the Banach space you know differentiability inverse function theorem Banach space is the only book I have seen then there are books of you know Rodin, Rogar's okay my own three books are there basic complex analysis elements of different topology basic algebraic topology there is a little Booh very elementary Booh and very readable Booh Satish Chiralee and Hari Krishna Vasudeva on metric spaces then there is a paper here and this book is for example it's like a bible for me this is also one of my favorite book in when I was in MSA then this teen and seabag it's like a this is like a reference you know it's like a dictionary of all count examples also this Willard's book similar to Dugunji's book quite respected book okay another important aspect of this entire course is that some of these symbols are frozen what does it mean that I am not going to use these symbols for anything else like if I say X is a topological space X could be a set X could be a subset and so on this is general notation right A, B or little X and so on but these symbols they are all in Euler font are space of real numbers C space of complex numbers Q space of rational number 33 ring of integer this n is set of natural numbers j power n minus 1 to plus 1 the interval taken n times the product minus 1 to plus 1 so similar just i is a closed interval 0 1 dn is closed unit disk in Rn okay for example if d equal to 1 then this will be a closed interval from minus 1 to plus 1 is an open interval here Sn is a unit sphere in Rn plus 1 Pn is n dimensional real projective space don't worry if you don't know these things but these things have been introduced in part 1 also C Pn is a complex projective space then I have this standard notation here because quite often I want to treat R the real numbers and complex numbers together so I have this standard notation k for both of them so whether it is real numbers or complex numbers depends upon the context if it is very specific then I will write R or C otherwise it is k it means that you can take either R or C okay so thank you for your attention and once again I welcome you to this course thank you very much.


My name is Charles Cornell. I'm a professional jazz musician and I've been challenged today to teach one concept in five levels of increasing darkness, increasing complexity. The topic I've chosen to discuss today is making a living as a jazz musician. I play instruments and I make a living playing instruments. Do you have do you have a guess as to how much money I make? Zero? Is that because I'm a musician? Yeah, yes. Do you think you might want to be a musician when you grow up? No. Why not? Because you don't think you're going to make any money? Well, that hurts. Do you know what it means to play music for a living? Isn't it like when you play music for money so you can pay for stuff? Yes. Yep, that's exactly it. Yep. Have you ever thought about playing music for a living? Well, no, never. No? Well, why not? Isn't it like almost impossible to make a living playing music?  I'm doing what I love to do and doing what you love to do if you can't make a living. Well, you know, it's not always about that and sometimes we'll accept maybe a less ideal scenario because we love it and yeah. We're here to talk a little bit about how you can do that in sort of a business world, like how you can make a living playing music. Do you play an instrument? Yeah, I play the drums. Drums? Cool. Very cool. Do you play in a band? Yeah. Yeah? What kind of music do you play? Like rock and like, yeah. Very cool. Very cool. Well, I play jazz.  I mean, you're probably gonna make money a lot better than I would, but just keep doing what you're doing, you know, and I think you'll be perfectly okay. Yeah. How's it going? Good. Good. How are you? Cool. So, you're in college, is that right? Yeah. Yeah. What are you majoring in? Jazz performance. Jazz performance? Yeah. Yeah. We're gonna talk about the music business. The music business. Right. Yeah. Well, you know, you can definitely teach to make some extra bread, you know. So, you know why we're here? We're here to talk about the business of what I do for a living. Yes. And what do you do for a living? So, I'm a musician. Oh, oh my god. I'm so sorry. That's rough, man. That's a tough one.


My fellow Americans, I'd like to talk to you today about the deep desire we all share to keep America free, secure, and at peace. In three days' time, American and Soviet negotiators will meet in Geneva to explore ways to reduce nuclear arsenals and lower the risks of war. No issue concerns me more, and none has taken up more of my time than our quest for a breakthrough on arms reductions. I do so willingly because as your president, and as a husband, a father, and a grandfather, I know what's at stake for everyone. And I'm pleased that the Soviets, after staying away for more than a year, have agreed to return to the bargaining table. The renewal of these negotiations is an important step in the right direction, and America will be ready to move forward on all promising avenues for progress. As I speak to you, our team is in Geneva. I cannot think of a more welcome message to give them than a strong vote of confidence from you, the people, and the Congress. I know that all Americans stand four square behind our negotiating team and wish them every success. In fact, you're the reason that the Soviet Union returned to the negotiating table. The Soviet leadership has seen your patience and your determination to keep America strong. They've seen the renewal of your spirit and the rebuilding of a robust and expanding American economy. They know we're going to continue moving forward to protect our freedom and our way of life. I want to believe the Congress will follow your lead, but that's not yet certain, and I need your help. Each House of Congress will soon vote on an issue that will directly and perhaps dramatically affect the outcome of Geneva. That vote concerns the modernization of our strategic forces with the MX peacekeeper missile. Let me take a moment to explain what that vote is all about. Nearly two years ago, after a decade of indecision, confusion, and endless debate over the merits of modernizing our aging land-based strategic missiles, our political process forged a bipartisan consensus that united us in our common search for ways to protect our country, reduce the risks of war, and work for dramatically reduced levels of nuclear arms. The MX peacekeeper missile has been part of the consensus and with good reason. Time and again, America exercised unilateral restraint, goodwill, and a sincere commitment to arms reductions. As a result, many of the missiles protecting our security at this very moment are older than the Air Force men and women taking care of them. They are missiles of the 60s, originally equipped with 1950s era technology. It's sort of like a 1963 Jalopy with some new parts. You know as well as I do that in many states automobiles that old will soon qualify as antiques, but the Soviets don't deal in antiques. Their response was the same as it's always been. No restraint. Just build, build, and build. While we debated and delayed, they developed three new types of land-based intercontinental missiles, and they've added eight to their arsenal, 800 new missiles with more than 5,000 nuclear warheads. It took us too long to realize there is no easy, cheap way to buy security. In 1983, based on the recommendations of a distinguished blue ribbon panel, the Scowcroft Commission, the Congress joined with us to approve the MX peacekeeper program, 100 up-to-date missiles that will replace aging Minuteman missiles. Since that time, the MX peacekeeper has finished seven successful flight tests, and the Soviets are back at the bargaining table. Well, once again the moment of truth is at hand. As I mentioned a few minutes ago, each House of Congress will soon vote on whether to release the MX funds they approved last year and continue production of the missile. The Soviet leadership views the current debate in the MX as a key test of American resolve. If the Congress acts responsibly, our negotiators will have a chance to succeed. But if we don't have the courage to modernize our land-based strategic missile systems, the Soviets will have little reason to negotiate meaningful reductions. And why should they? We would be signaling to them that they can gain more through propaganda and stonewalling than through serious negotiations. The time is now to send a signal loud and clear that a united and resolute America backs our negotiators at Geneva. And that could be the real key to a successful outcome. My fellow Americans, the stakes are so very high. The vote on the MX peacekeeper isn't a budget issue. It's about our nation's security. And when it comes to protecting America's security, we can't afford to divide ourselves as Democrats or Republicans. We must stand together as Americans. It's up to you to let your feelings be known. Your voice matters. Let it be heard. Until next week, thanks for listening and God bless you.


OK. So here's the algorithm. We take as input an elliptic curve of the form y squared equals f of x, and in the code, I'll even assume that it's in short virus stress form. We already dealt with l equals 2, remember, so we know l is odd. And our goal is to compute the trace-for-meanus mod l. So step one is to compute the L-th division polynomial. That was our h. And there's standard recursion formulas for doing that that you can find in Silverman's book or any book on elliptic curves. The recursion formulas you need to compute these division polynomials. This is a very straightforward thing. Step two is to compute the Frobenius endomorphism restricted to the L-torsion, which we already saw to do that, but just x to the q mod h. Of course, we don't actually compute x to the q and then reduce mod h. We think of x as living in our univariate polynomial ring mod h, and we do binary exponentiation there, just like we did when we were finding roots of polynomials. So that when we're computing x to the q, we never see a polynomial of degree more than twice the degree of h, because we're always reducing mod h at every step during the exponentiation. Similar, we exponentiate our cubic polynomial f to the q minus 1 over 2 power, again, doing all the computations mod h as we go. And then once we're done, we use our multiplication law for the anamorphism ring, our composition law, to compute pi l squared. So we don't even need to do raise to the q power twice. It's better. We might as well just use the addition law or the multiplication law in our anamorphism ring. The next step is to use scalar multiplication with a binary double and add approach to take the one scalar multiplication we know, multiplication by 1, and turn it into multiplication by q. And then we'll compute one side of the equation we're trying to solve, which is pi l squared plus q sub l. Those are the things we know. And then we're going to iteratively compute 0, pi sub l, 2 times pi sub l, et cetera. Each of those coefficients corresponds to some c. C is going through 0, 1, 2, 3. And at some point, guaranteed to happen before we hit l, we will find a c that works, that's such that c times pi sub l is equal on the nose to pi l squared plus q sub l, meaning the a's and b's in our representation of anamorphisms match on the nose. Now, it could happen that during that step, or even during the scalar multiplication of one step, it could happen that we hit a non-invertible denominator. If that arises, just update, replace h with our better h, and go to step 2 and start over. And if we ever get down to the point where, I mean, eventually, we're going to get down to some irreducible factor of h. So this is that we can't just keep restarting forever. Because every time we have run into a problem, we have a proper divisor of h. And then at the end, we output our trace-verbenius model. So let's go ahead and pop into the code. And yeah, maybe we'll look at the sage version, even though it's a little longer. One of the reasons I've been tending to show the magma code is because you'll see the same function in magma tends to be a lot longer in sage, just somewhat because of the way the spacing works. But I know sages and Python are familiar to more people in the audience than magma. And I really want you to understand and appreciate this algorithm. So I'm going to go for the setting that I think is the most familiar to everyone. OK, so our first step, the first cell in this notebook, which I encourage you to check out yourself when you have a chance, is just implementing all the operations in our endomorphism. We need to know how to add and multiply. And we need to implement a scalar multiplication explicitly doing a double and add. So the addition is the first step. And so what does the addition function take in? It takes a p and a q, which you could think of as, quote, points on our elliptic curve over this weird ring. And so what are p and q? They're each a pair of polynomials, the a and the b, that represent that endomorphism. The y is implicit, so we're not passing in any y's. A is the a in our curve equation. y squared equals xq plus ax plus b. Because if you recall from the formulas for the group law when you're doubling a point, what a is.  Because there are also situations when you're applying the group law where you need to know what f is as well. OK. And in particular, f showed up in our r. So the first thing we do is we just pull out the components of p and q. So a1 comma b1, a, these are the univariate polynomials mod h, a1 and b1 that correspond to p, and a2 and b2 which correspond to q. If a1 and a2 are the same, meaning we're thinking of this, we have endomorphisms that do the same thing to the x-coordinate. Well, then we want to check and see what happens to the y-coordinate. There's only two things that could happen, either they're the same or they're opposite. Because our elliptic curve looks like y squared equals f of x. If I have the same thing on the right-hand side, there's only two possibilities on the left. If they're the same, we should call our doubling routine, which has a slightly different operation, which we'll see in a moment. But if they're different, we get 0. We're adding an endomorphism to its negation, and we get the 0 endomorphism. And we'll represent the 0 endomorphism as just an empty tuple. And so you'll see at the very first line in the addition law, I had an if not p or not q. That's just checking to see if p or q is 0. And if it is, just return the other one. We know how to add 0 to anything. OK. So now we've dealt with all the special cases. Now we're going to get to the actual addition. The first thing we need to do is compute this m that appeared in the group law. This is the slope of the line between p and q on our elliptic curve. Now that a2 minus a1, that's some polynomial mod h. And it's possible that it's not invertible mod h. So that's why that line is inside a try accept clause in Python. This is how you catch an error. So the sage, I should say this is not just Python. This is sage, we'll raise a division by 0 error if a2 minus a1 has a non-trivial GCD with h. And if it does, we're going to capture the thing that gave us a problem, a2 minus a1. And then we're going to raise the error again. And this is going to go all the way back up to the collar. And we'll see how the collar handles that error when we get to it. OK, but from the point of view of the addition operation, we're done. We're like, yeah, we ran into a problem. We know we need to reset and start over with a new h. So we're never going to add these points. Let's just get out of here. And so that's what that raise does. The raise, x, it's the function. Assuming we are able to invert a2 minus a1, then we compute a3 and b3 using exactly the formulas I showed on the slide. And we return the pair a3 comma b3. Notice the computation of a3 and b3 only involve addition and multiplication. We don't have to worry about any errors there. It was only the computation of m that was potentially problematic. This is all happening in the quotient ring. A and B are elements of fq bracket x mod h. I'm not modding out by the curve equation here because we've now sort of made the y implicit and we're going to explicitly deal with any situation where we get a power of y greater than 1. So we're actually the algorithm, the implementation. Mathematically, we're working in this two variable ring modulo, this ideal with two generators. But in the algorithm itself, we're always working in a quotient of a univariate polynomial ring. Let's take a quick look at the double, which is very similar. If we're doubling 0, we know what to do. That's 0. Otherwise, we take the coordinates and we try to compute m again. This is the slope of the tangent line. And again, we might find something that's not invertible. And if it is, we catch the error, we record the polynomial that was uninvertible, and we exit out. We raise the error again and it'll get caught further up the call stack. But if things are in good shape, we apply the formulas to compute a3 and b3 and we just return a3 and b3. Now that we know how to add and to double, we can implement our scalar multiplication, our double and add scalar multiplication. And this function here should look completely familiar to you if you've ever implemented binary exponentiation. It's exactly the same algorithm. I'm doing right to left exponentiation, I guess, working from the most significant bit down. But it's just executing a double and add. And so you can see the scalar multiplication itself is completely generic. All the work is being done in these steps. In the double and in the add. I should scroll it up a bit so it's easier for people to see. And then lastly, we need to know how to multiply an anamorphism ring. And I promised you this would be one line of code and here it is. And this is just implementing the composition of the a1, b1, and a2 in exactly the form that we need. The lifts are just there because we want to do the composition working in our univariate polynomial ring and then we reduce back down to our quotient. So all of the composition and the reduction mod h, all that's being magically handled by our computer algebra system. And this is what I meant when I said that Scopes algorithm is hard to implement if you need to do it with your bare hands. But if you've got a computer algebra system that your back can call, it's quite straightforward. So we've now implemented arithmetic in our anamorphism ring, our L-torsion anamorphism ring. And actually, these functions have other applications, not just in Scopes algorithm. If you're ever working with isogenes or there are a lot of scenarios where you might want to use these exact same sort of things. But now let's move on to the heart of Scopes algorithm, which is computing the trace mod L. OK, so we take as input an elliptic curve and an odd prime L. We're trying to, and we're going to return the trace of our binius mod L. Step one is let's just figure out what ring, what finite field we're working in. That's what ff equals e dot base ring is doing. And this assert here is just making sure that the caller didn't violate the assumptions that we said we were making. The J invariance, not 0, 7, 10, 28. And we want the characteristic to be greater than 3, just so we can fit our curve in the form y squared equals xq plus ax plus b. Those are not necessary. You could make the implementation a little more complicated and handle these cases. Then we're going to pull out q, the cardinality of our finite field. We're going to form the polynomial ring in one variable t over our finite field. We're going to grab the a and b from our elliptic curve equation. And if L is 2, we're going to implement the algorithm we already agreed was very straightforward. We just checked to see if f are x cubed plus ax plus b. And now we're working in this polynomial ring over the finite field. And so I've called the variable t. If t cubed plus at plus b is irreducible, we know the trace of hermeneus is odd. And otherwise, it's even. OK, now we're in the case where we have an odd L. And we're going to compute the Lth division polynomial. And we're going to make it monic. I mean, the definition of the division polynomial, there was going to be an L squared out. And the numerator L doesn't divide the characteristic of our field, though, so we can make it monic by dividing through by the leading coefficient. And Sage has a built-in method for doing that. All right, so now we've done all the setup work. We're now ready to enter the main body. And in order to handle the fact that we may need to restart, I've encapsulated the whole algorithm inside in what looks like an infinite loop, while true. OK, at some point when we succeed, we're going to return our value out of that loop. But we want the while true there to make sure that it will automatically restart when we get into trouble. And we're also going to keep everything inside a tri block because we need to catch the error that was re-raised in either, it might have been caught by the add and double and then re-raised to report the non-invertible polynomial mod H. OK, but let's, for a first pass, let's just assume everything goes as planned, and most of the time it will. So the first thing we do is we compute our quotient ring mod H. That's what this step is doing.