What's going on everyone? Sam here with late in sports cards ripping 22 top stadium club chrome baseball Hobby 16 box full case break number two random division style There's a look again at your random results as always you can find these on the website under the results tab as well as the Lincoln chat So the reason why I'm giggling is because I Just asked a trivia question What what pitcher has the most career wins without a single like at bat? And for some reason the first person that came out of Jake's mouth was cliff Lee Lee What? No, it's not Pedro by the way. It's definitely not cliff Lee He goes it's not cliff Lee No, you're right. It's not I said she should should be sent home after that that manual class a base Team of the future Peter Lanzao Team of the future Bobby Whitrup. They're Jeremy Guthrie. Yeah, there you go. Jeremy Guthrie. Yes. It is actually Ron Ron Gidry stop there legal trivia is done trivia's canceled That I'm sorry to disappoint you show we got a redemption It's gonna be a Mike Trowell base card autograph AL West there you go Jared. Congrats, buddy Trout coming your way. Let's go big hit right there will Clark and Joe Adele Royce. Lewis are legal. Definitely Absolutely, that's what happened And There's a Glaber Taurus to 199 on the blue Brandon March rookie auto for the AL West So morale is Aaron Ashby was that just like a shot in the dark illegal the disrespect To what Rod Gidry Yeah Abrams refractor rookie he's just jealous Me I am I don't have the legal's knowledge He wishes he was a beam team one soda. I wish I was in the same room as someone whose first guest was Cliff Lee To that question certain someone carried you to a Wednesday true Orange Ozzy Albie's to 25 for the Braves nice one man And I'll East Me and I wouldn't say either of us. We both accounted for three runs. Yeah beam team Abrams and I'll East Siebold and base Bobby by as refractor MJ Melendez nice one there for the AL central. There you go Greg. It's MJ He's actually kind of a beast solid for sure. So the low big wabba Future Jake shirt Jersey That's his nickname. Oh Jackson a 199 really? Really I was spent a trope was in beam team. Okay, sure Yeah, MJ is a stud so you saw Josh low is yours. You're sorry gold Dale Murphy to 50 and at least And what? Oh, I know they're their brothers Nate and just really yeah, oh, I didn't know that that's pretty cool For Jones, I guess I never put two and two together Well, I just was kind of what's that when they traded me cuz like Green Simon musiati rookie for the NL East to 99 Those stories are Lucroy or Jason Kipness Me Jason Kipness. I'm gonna go Kipness Kipness there. Yeah, Miguel Cabrera beam team Kipness, yeah Beam team Acunia base And he was like better in his respective position Jesus Lizardo Josiah Gray Hello, Jonathan Luke or he was solid destiny jazz beam team wave is Vladdie jr.  That's awesome That's pretty cool. Honestly, though, Anthony That's pretty cool Beam team Tatis brash bold and brash more likes belongs in the trash Not saying that to Matt brash. I'm saying that orange Carlos Santana to 25 Apparently like my my college roommate like His like coach in high school at the high school baseball was like good friends with Carlos Santana There is one day that he like Carlos Santana went to my buddy's high school to like train with the baseball team And my friend was my roommate was sick that day O'Neill Cruz so I always make fun of him about that. We're like he's like, oh, that's my boy Jonathan or Carlos Santana We're like, well, he never met him There's Tommy Romero AL East Nice one there. So if you had to show that Zach Lug Fracture Michael Kadiar JJ Hardy. I mean, I think Hardy was better But I think I like a dire better because I told this to somebody but Michael Kadiar is a he's apparently a really good magician Remember there was a thing on like MLB TV where he was doing like magic tricks There's a ref I've never seen that That sounds pretty funny Blue Shohei speaking up to 199 Dynasty at Manny Machado wave team team says Suzuki Pull it out on your rookie five spots JJ Hardy was kind of a dog though. Yeah with the Orioles Really good like 2010 Orioles yeah, like the ALCS Orioles Like him Adam Jones Machado a good Chris Davis trumbo Like bunch of studs there What he I think Trumbo was like I came up with the angels right Trumbo was there when Even the future J rod Now we sleep we sleeved it we still sleeved it Rory Robbie Grossman to 199. I don't realize I knew the PSA 10s were doing I didn't realize the base were doing like over 200 a piece. That's wild Yeah, dude, they're doing like 300 The base Ohtani rookies from blowman chrome. Oh my god. Yeah Wade Boggs Gracefully gave it a penny sleeve Spencer Strider the team of the future Ohtani beam team trout Yeah, the papers are doing like 30 dude the base papers from regular Bowman nuts silliness silliness Team of the future Peter Lonzo wave beam team hunter green rookie beam team green Spencer Trollkelson auto Reinvalade for the Rockies Nice one there NL West Kirby Puckett RIP beam team judge Green Joe Adele to 99 Angels Abrams not cliff Lee Yeah, good statement good statement Spencer Trollkelson refractor Correct jay correct. It is not Robocopper Nicolio of Nicolio Kitch's brothers, dude beam team Harper. This is Simon Muzziotti refractor rookie for the Phillies NL East on that one flu Rylan Bannon To 199 a least Green Alex Verdugo to 99 for the AL East Krauss judge judge Team the future break our Kyle Tucker Current Jake Scherzer's he Brandon Lau Yeah Gold Cabrion Hayes nice one there 250 extra auto grads a NL central you to see It was a rookie it's like last year Last newt bath Jayrod rookie is also a beam team Otani Leave that one to Forest did you hear the great cliff lead debacle? I would last now refractor There was a cliff lead debacle big time Wanda Franco team of the future will you present for that forest because you need to be or say yes You need to be Educated on what just happened here So I asked a trivia question I asked the trivia question What major league pitcher has the most wins without an at like without an at bat without a career at bat in The first guy that came to Jake's mind. He goes, it's not cliff Lee Yes, it was not cliff. I Was thinking I was going through my mind beam team Wanda Franco rookie Brainstorming something Donnie with Donnie doesn't know who cliff Lee is Blue Danes v. Swanson a 199 Never gonna live that one down Gold JP Crawford the AL West to 50 Yeah, yesterday Donnie was like not yesterday Wednesday, Donnie was like, oh the Yankees finally got some points George Kirby for the AL West You say yeah AL West nice one there Jerry Matt or George Kirby I was like, they're not called points my friend. They are not Blue Mike Clevenger at a 199 and I'll West Then everybody just starting light just lighting them up beam team rookie Bobby Whit jr Wander rookie Torkelson team of the future will clerk Carlos Kalea is a green Clayton Kershaw to 99 for the NL West I think that's worse Kenzie. I think that's much worse. I think that's much much worse Yeah, why Kenzie said see why I mean That's that's understandable. Yeah, for sure. I mean cuz Tori Huntser Give yourself some credit. No, I think I think that calling Calling runs in in baseball points is pretty bad is is is worse Ty Hilton back in the day. Oh, yeah, they probably did. That's that's the the crazy part I'm sure they did call him Ty Hilton, especially during like the draft process and everything. So like Ty Hilton Julio Rodriguez beam team Hunter Green team of the future Brian de la Cruz rookie auto for the NL East Adrian Martinez refractor rookie. Oh, yeah, forget it dude Yonis his name Good god Destiny Bobby Whit jr. I think you believe that guy was the worst like the lowest player rated in 2013 Was Yonis and like Rudy Gobert one year was to Alfonso Reeve us and Alcentral to the NL central Logan Gilbert face Team Peter Lanzo. I don't understand that what Yeah, no, exactly I get that because they're all like everything's like abbreviated. Yeah, you know Everything's totally abbreviated With the Barbie eyes. Yeah, you're right. Yeah, Lou IKF. Why does he have a card in this? I say a Keener-Felefa a L East to 199. I really made you mad. I mean if I was making stadium club I don't think I KS would be like a guy that I push to have in here to be fair Yeah, trade it like so good whites and three days max box Hey, what's up Cliff on 10?  Why they have Kyle Hendricks batting. I don't get it Throwing me off here blue Walker Bueller 199 NL West color match there Josh low big wava Legals versions of Yanis was tagged for review. Oh, man Yeah, well, they knew it was they knew it was illegal saying something so they probably did that just to be sure probably like yeah Keep an eye on this guy Even team O'Neill cruise rookie Orange runs he contenders the 25 NL central See see there you go see Auto ban the new super high on the island of vanished Hmm Bobby with junior team of the future. We got a mod Jake You are on the baseball I'm gonna unmod you on the baseball channel next time I'm breaking over there. I I don't know I didn't do anything Yeah, that's that's grounds enough to be unmodded grounds enough Philadelphia Philly Cliff Lee not having any at bats Hey, it's me very wasn't primarily known there. How do you call it was an Oriole fair? Fair Heather fair. No, it's even better. Is that was the first thing I thought that's being on Was the Phillies and you said it's not. Oh, is that why you said it's not. Yeah, it's not Cliff Lee But you know, I still felt the need to you know, bro his name in the ring in this conversation here Respectable picture Yep, see that Green Matt Veerling those those talking about nice one there for the NL's NL East. Yeah, Jake was telling me about that earlier for us. That's pretty funny. See you in here Illy, yeah, can Lee Janssen Beats me Austin Riley blue to 199 for the NL East green is Mark Kola's Vari nice Did I probably Nice one there. Why are we named after things in nature cliff and forest? Yes, it is red three and five team of the future Ronald Acuna for the NL East mr. Acuna Juna Mr. Acuna Juna That's when they're NL East. They're the NL East Michael a there you go Michael. I didn't know what regular I didn't know what the regular Anthony named after a piece of furniture. Oh boy Jake burger a fracter rookie Matt Brash you like our sponsor O'Neill cruise rookie potential non refractor refractor Of course my boy In the future will Smith it's cliff Lee isn't it beam team CJ Abrams Rickle Bold statement for us up gold Steve Carlton the NL East of 50 There's the doll Bruhan future Jake shirt Jersey at least The doll Bruhan Anybody has a flow out against the position player. That's bad. Okay. He flew out to right field. That ain't good Wave beam team Freddie Freeman. I don't like to hate on players, but come on, dude Yeah, it's position player ain't great Great Jeremy paying you a rookie All the young nowadays Torque blue Brandon Crawford to 199 NL West Have you in base Eric Davis murder grinding for Orioles Eric Davis in the show 21 Do he has a card? In the program The shirt You know where they have like the charisma with like the cool like yeah, that's that one Blue Matt Manning to 199 a l central J. Roderick beam team niggie They're dead beam team Tati's. Oh, this mom has Horace That's exciting. She has like old football and baseball cards. That's a trope of them Same forest same boat, dude same boat Anthony that's funny, dude Lucius Fox. I swung there for the NL East green Carlos Correa to 99 The a l central Wander rookie on the back there Soto beam team say a Suzuki beam team rookie Kyrie moons. There's a Randy Johnson for the AL West I know he got mixed in a water Anthony mixed in a water Jake needs to mix in water, too There's team of the future Lou Bob wave beam team trout. It's got to be a cylinder, right? Chuck Peterson 250 Pretty good Well, it's definitely not clifley sure just like right here a factor rookie Andre Jackson Fracture rookie auto for the NL West. That's all good You know what it was there's just process of elimination. That's all it was you eliminated clifley to be fair It was just not I shouldn't have said it. It was pretty funny Well, it's not clifley Can take that one off I want you to look that up actually if it's more than 170 I will stop laughing at that being a bad guy Yeah There's blue Kyle right to 199 143. All right, that's not a terrible guess then I guess Theoretically his prime prime wasn't with the Phillies like he was very good in Philadelphia tray Turner Green to 99 it still says prime. It's probably what Cleveland, right? Cleveland or Well, it's like Texas We stunk in Seattle, right? I didn't give him a huge deal. Yeah, I would say Cleveland Cleveland Nick Allen AL West rookie auto Wanderfranco destiny, right? See in the future. Shane Bob's rookie. There's an orange will Clark color match for the NL West to 25 Will Clark Clark the shark Under 100 I can confidently gonna say he had under 100 wins in his career. Well, am I right? 107 George Springer 120 100 green beam team, that's kind of wild actually But he had that many wins actually played for a while And base where you go here guys. He has more losses than it is. That's Really bad There's a hundred and seventeen losses and a hundred thirteen wins. That's like impossible But he has a career war of What 20 pretty good actually He almost has 2000 innings, but he's 130 short hunter green team in the future. We need a big about a ball Don't let us go in the show You got to be my show guy attacks when we see new stuff come out Yeah, you need to inform me to when new stuff comes out. I probably won't be ahead of the curve like you the stupid old man blue Elliott Ramos to the NLS to 199 That's that's gonna be that's gotta be under What's it like 98 How many losses That's Probably single-handedly, yeah, so close in team in the future Probably like single-handedly fueled by that one game on the green Oh my god, what? Six Luke Williams the one 99 you pitched one game. Oh god TJ Friedel going to the NL central rookie auto God, it's got to be like like nine under rent for more 13 17 30 More than 50 It's a beam team Otani more than 50 90 I heard the night What does he are just give it to me 135 135 ERA point two innings pitch ten and runs Oh my god, dude ten earned I remember like as soon as you got pulled out of the game. He posted on Twitter on the time It's like I don't got it in me anymore team teams faster to focus and I can't go point two three innings give up 10 100 what was it again on 135 135 my god, that's like I think I can go out there and Be a position player and not give up that not have a 135 ERA 15 with 81 hits for nine For nine 54 for nine. That's that's the truth. That is like vomit-inducing stats right there show a Shopee Hunters That's what I'm saying because I feel like I'd probably give up at least six runs like At easy But I think I can get through three innings beam team wonder Franco or not three I think I threw one inning without giving up ten Because I got to get like an easy ground out or a fly out or something like I'm not gonna strike anybody out Obviously, but I think if somebody can like just miss one Let's go cranky My guy griffy refractor that guy's a dog. There's Royce Lewis and L central or a L central a L central I love that cranky Yeah, I have a time-backed cranky Jersey Green Byron bucks into 99 pretty sick You guys ready for my Hibachi shirt Jersey that's in the mail currently Torples in the destiny Agent zero baby. Let's go Magic legend Gilbert Arinas CJ Crone to 199 It's a tops now moment legend CJ Crone Beam team Bobby Whit jr. Let's see if there's like a rent just look up like random baseball player All right, it's probably gonna be like legitimately like known to players But see if you can get like a really random one John Durant orange Matt Olson for the Braves and Elise nice one there That's sweet 25 that's gonna be nine of 25 Very cool Brian Hayes and John Crook Let's talk about finding some lost legends in here David Ortiz All right last box the case guys. Good luck. Thanks for your patience here as well got one more short break after this Just a Star Wars random hit style take about max 10 minutes So you want to stick around The last break feel free to do so Kyle will still be over on drip for another about two hours I believe you'd like a personal Look at that balance What a throw dude you find one or no Pedro is awesome. I Got like the very tail tail end of Pedro's career, but I did like Pedro and I was younger I didn't like him when he was a red sock obviously, but beam team J rod rookie Boston beat up on Detroit today Are they like legends and stuff Brandon Nemo went down She had a good one. It's a no player, but what is this picture? Like a computer like generated Terrifying Beam team Joey bottom think we all remember him as a Philly. Oh, yeah, so he has best years Brooks Robinson in 99 Shane boss a Elise nice rookie otter there on card Shane Bieber to 199 beam team Peter Lanza Gabriel rice Gold Andrew Benintendi as a Yankee to 50 Got that was an era last pack of the break. Good luck everybody The asterisk twice that is kind of wild and Jerry Pena rookie do a quick recap here everybody just of our autos Some of our little numbers. We've got Royce Lewis Andre Jackson Josh Winder Brian De La Cruz TJ Friedel Nick Allen Shane boss Lucius Fox, but all Bruhan George Kirby Simon Muziati Ryan Belade Tommy Romero MJ Melendez Brandon Marsh Matt Veerling Cabrion Hayes Matt Olson Back to the future red to five Ronald Acunha and a Mike trout base card auto for the AL West that'll do for the break guys. Thanks again for the film. That's up Star Wars last break tonight


Autolight and its 96,000 dealers present. Suspense. Tonight, Autolight brings you the story of a man who would live as long as he kept talking. Tell you why I shouldn't die. Starring Mr. Richard Widmark. Hi, Hap. Spring fever? Yeah, Harlow. I just can't get going. Well, too bad you aren't in Autolight's day full battery, Hap. The battery that needs water only three times a year in normal car use. Some starter, eh, Harlow? You bet, Hap. Thanks to its rare, right and rugged pep and power. What's more, it gives longer life as proved by tests conducted according to accepted life cycle standards. You mean that, Harlow? I sure do, Hap. Because the Autolight's day full has fiberglass retaining mats protecting every positive plate to prevent shedding and flaking and preserve the power that's packed into that paramount provider of perfect propulsions. You sure pep me, Harlow. So, friends, see your neighborhood Autolight battery dealer and ask him for an Autolight stay-full battery, the battery that needs water only three times a year in normal car use. And remember, you're always right with Autolight. And now, with Tell You Why I Shouldn't Die and the performance of Mr. Richard Widmark, Autolight hopes once again to keep you in suspense. All right, Nat, make your pitch. I got time. Charlie, it's good to see you, Charlie. How about a drink? Is that the best you can do?  Haven't you got a pitch to hand out? How your pure is the driven snow and everybody else is wrong? Oh, come on, sell me a big order, Nat, because I got time. Plenty of time. I gotta wait till the cops get here. Don't let them make everything perfect for you. We got lots of time, Nat. Now, listen, Charlie. Oh, that's no routine. Please, Nat, give me the routine. Make me mad, real mad. Charlie, you're a friend of mine. For friends, I haven't got a routine. You always got a routine, Nat. You're a pitch man. Pitch.  You got a gun, you stand there. The gun's pointing at my head. Everything's just dandy.  And why?    But you're not sure. You're not sure you got all the facts. You're not sure you didn't get everything twisted up.  Now, Charlie, I want you to go back a few weeks. Back to that night when you and Eileen were in her dressing room. Sorry to bust in here, kids, but there's a little thing I'd like to take up with Eileen. Do you mind, do you, Charlie? No, I don't mind. I'll be in a wings, Eileen. Eileen, I just got a couple of tickets to the roulette on fifths. Well, a bunch of new acts. Not tonight, man. Look, their act leaves in a few nights. You're gonna be working. Now, if you don't go tonight, you'll miss it, and show business is your racket. You ought to be up on all the new things that come around. But I promise, Charlie, we'd maybe go to a movie.  I'm not out to escort you man and dame. I'm merely posing a professional problem. Do you or do you not want to catch the greatest new act that ever was put on a stage? Sorry, Nat. Okay, that's the final word. But you know how you wanted to see Elmira Shoe in the four laughs. Are they playing? Last night, Saturday. All right, Nat. I guess it wouldn't hurt this one night. Atta girl. I'll be ready at 7.30. 6.30, we'll snag a meal. 6.30 then. So, well, see you tonight, honey. Now, it's true, I took her out just a second. Now, Charlie, put that gun down for a second. Let me finish. There, that's it. You see, it was a purely professional evening as far as intention is concerned. However, that does not alter the fact that something happens between a man and a woman. I'd be a fool to tell you I didn't feel a great deal of affection for that evening. I did, but it is also true, my friend, that it takes two to make a romance. Eileen came along very nicely. Now, let me ask you something, Charlie. Would you want a girl as your wife who was as susceptible to romantic pressure as Eileen was? Can you honestly and truthfully and with any sincerity say yes to that question? The answer's obvious. Of course not. To continue. After the show, I took her up to her place. We had a drink, she turned down the lights, she turned on the radio. She did, mind you, I just sat there. Then she came over, sat down next to me. I feel guilty, Nat. Guilty as sin. Why did you lie to me about that act being at the roulette? What's the difference? You had a good time? I feel guilty. Well, you know, Charlie, all alone. You love him? I think so. I'm almost sure. I just want a little time. Eileen, you're kidding yourself. You don't love him, you never could love him. He hasn't got any class. He used to be a fighter. He's got a crease in his schnoz, your miles above him. He's gentle, he's sweet, he's kind. Look, you talking about a man or a house dog? More than that. I never met anybody like Charlie. He worships me, he'll do anything for me. I mean it, Nat, he actually worships me. Unhealthy. I don't know. Look, would you indulge me for a moment? Strictly for demonstration. Depends what? I'm gonna put my arms around you. Like this. Okay, so far so good.  Don't say anything, don't want to hear a thing. What now? Kiss me. Nat, you're the greatest pitchman on the island. I beg your pardon, this is strictly demonstration. Kiss me. Fine. Now, I, uh, I've been frank with you. I want you to be frank with me. Was that A, better? B, worse? C, similar to Charlie? Don't answer right away. It was better. Oh, man. Eileen, you don't want Charlie. No. You want me. You want me more than anything else in the world. Yes. Eileen, I'm nuts about you. Oh, kiss me. Now, Charlie, would you consider me a well-adjusted individual if I went into that apartment and failed to make love to Eileen? Would you believe me if I told you I tipped my hat, said goodnight at the door? Certainly not.  I could hinge every story in the book. And what would it get me? A bullet through my head, right? Right. Therefore, you're going to get the truth. After that evening, after we decided we were going to get married, we went to you and informed you as to our plans. If anything had been more on the level, Charlie, ask yourself that. And then I sent her out. You remember our conversation that time. I'm going to break your neck. Hold it, hold it, Charlie. Now, you listen to me. Eileen and I are in love. We've been in love for a long time. We're going to get married. You work your spiel on. Are you in your fast talk?  Charlie, Charlie, Charlie, Charlie, sit down. Have a drink. Calm down. Now, you want to suffer? Living your life with somebody you could never love you? She told me she loved me. She told me she told you she didn't know herself. She was trying to let you down easy, Charlie. Now, it's tough. It's very difficult to accept the news. I know I've had it myself time after time. But, Charlie, a little pain now is a thousand times better than a lot of pain later. Agreed? What are you trying to do?  That girl is not for you. She never was for you. Eileen is a show girl. Why, if I told you... Listen to me, Charlie. I happen to be the same kind of no-good type that she is. I am. That's why we go well together. I'm nothing but a Coney Island pitchman. That's all I am, a nothing, a nobody. But you've got something, Charlie. Something called heart. No, Charlie, you're way too good for our kind. I can't understand it. I had it all figured out. You mixed me all up. That is the true, all those things you said about her. Every single word, Charlie. We're too old to lie to each other. We've been friends too long. I never knew. I never knew. Now, don't worry, Charlie. The right one will come along. I'll be there to give my blessings. All the luck in the world, Charlie. You're a great guy. Much better than we'll ever be. Thanks, Nat. You're all right. We went to Reno to get married, as you know. Now, I could tell you she ran away with somebody else. I could tell you she decided not to go through with it, but nothing of the sort was the case. I left her in Reno. And why? Because I suddenly realized I wasn't really in love with her. You see, the night before I happened to meet this girl at the bar of the doorway in Reno. This other girl was your type, Charlie.  This is the girl for him. 9.30. Thanks. Another drink? No, I'd better get going. At 9.30? I'm supposed to meet somebody. You just got your papers today, right? Yeah. I'm a free woman as of tonight. Then who you're running to meet? Another entangling alliance? What's the point out of the frying pan into the fire? This is just friendship. That's how it begins. But you'll be worse than the other one. What about you? Me? You don't have to worry about me. Because of that girl you're with? My sister. Oh, sure. That's right. I really have to get going. Yeah, sure, sure. I understand.  Are you busy tomorrow night? What did you have in mind? Nothing spectacular. Just me. 6.30, a ride, dinner, a scene of that. It's a date. So he traveled around. Sure, I knew she had money. I'm no fool, Charlie, but you can't buy affection for money. That's one thing you learn in life. She'd have to have more than money as far as I was concerned. And I was as honest as anybody could be with Eileen. I sent her home to you. To you, Charlie. The fact that she didn't go back to you had nothing whatever to do with what I told her. So believe me, Charlie, when I got back to New York I was the most surprised man in the world when you came up to my place and gave me that piece of information. Nat, you gotta help me, Nat. You look terrible. I know. Look, Nat, I didn't know what I was doing. I saw her. I was like a madman. What happened? I heard she was coming to town so I waited for her and I followed her home and I did it. Did what? I killed her, Nat. I took my gun and I killed Eileen. The light is bringing you, Mr. Richard Widmark in Tell You Why I Shouldn't Die. Tonight's production in Radio's Outstanding Theatre of Thrills Suspends. See, Harlow, what rhymes with June besides moon? Uh, soon, Hap. And that's when you should see your neighborhood auto-light battery dealer for an auto-light stay-full battery. The battery that needs water only three times a year in normal car use. The sooner the batter, eh, Harlow? Right, Hap, because the auto-light stay-full has over three times the liquid protection of batteries without stay-full features to guard against one of the greatest causes of battery failure. That's why the auto-light stay-full needs water only three times a year in normal car use. And it's got other protection, too, Harlow. It sure has, Hap, because the auto-light stay-full has fiberglass retaining mats protecting every positive plate to prevent shedding and flaking and give longer life as proven by tests conducted according to accepted life cycle standards. So get ready for summer starts before summer starts. Yeah. And take a tip from me and visit your friendly auto-light battery dealer. He's equipped to give you the best in battery advice and service. And he's got your auto-light stay-full battery, the battery that needs water only three times a year in normal car use. Remember, you're always right with auto-light. And now auto-light brings back to our Hollywood soundstage Mr. Richard Widmark in Elliot Lewis' production of Tell You Why I Shouldn't Die, a tale well calculated to keep you in suspense. Charlie, when you told me that you'd killed Eileen, all the anger rose up in me. But then when I saw you as you really were a poor, scared guy who needed help, I pitied you, Charlie, as I pity you now.  Yes, Charlie, hurt deep down here. You made me do it, Nat. I'd never have done it if you hadn't made me do it. Now that's no way to talk, Charlie. Nat, you've always been my friend. You were the one who told me about it in the first place. You've always been the best friend I had, Nat. You've got to help me. Charlie, you're not going to like what I'm going to tell you to do. I can't give myself up. They'd kill me. They'd try me for murder. Charlie, there's no other choice. There is. A friend of mine owns a boat. Now, the same friend of mine, he told me that you were going with a girl and Reno had some money. You got some money, Nat. Give me 500. Look, I don't know where you're getting your information, Charlie, but I went out with this girl strictly because I liked her. Money had nothing to do with it. She never gave me one single solitary sense. And besides, do you think I'd allow you to become a fugitive? Do you think my conscience would ever let me alone, knowing that I sent you out into a life of hiding? Don't give me a pitch, Nat. All I want is 500. You've got a nice apartment. You've got a silk dressing gown.  All right, Charlie. Just to show you, I've got nothing but a soft heart. This will put you on... What ship did you say? The Mary Ann Frederica. Yeah, yeah, that's right. All right, this will get you on. 500, Charlie. You don't deserve it. You know that. Thanks, Nat. I'm sorry I talked that way. Now get out. You bet, Nat. I'll never forget this. Hello, Operator. Would you please be so kind as to get me the police department? Wait, Charlie. Please give a guy the right of explanation. Now, let's look over the facts. Number one, you killed her.  The man next door didn't kill her. My grandfather didn't kill her. You killed her. So that makes you a murderer. I admit very frankly that I did call the police. And why? Because I knew that if you ran away, they'd get you, Charlie. You'd be already convicted. You wouldn't have a chance. So you see what I did, Charlie? I took my life in my hands just to give you a chance at your trial. Taking the chance you'd think I was a double cross. Oh, Charlie. When they sent for me down at the station after you'd been picked up, when I saw you sitting there, those lights on you, your shirt opened and the sweat and your hair disheveled. When I saw that, Charlie, I cried. You didn't see that, did you? Oh, I did, Charlie. Tears were running down my face. And ordinarily, I'm not known as a sentimental man. Recognize him? Yes. Charlie, it's me. And that? You turned me in. What'd you turn me in for? Charlie, Charlie. Does he have an attorney? You'll have to ask him. Lieutenant, could I talk to you alone? Sure. Come on out here. Lieutenant, I've got a young lady waiting for me, so I've got to rush. That is, if you don't need me anymore. Just a few questions. Sure thing. But before you begin, could I make a small statement? It may be repeated in court. That's just what I want. Well, I went with Eileen for a long time. Took her to Reno. We were going to get married. But she came back here when we decided not to go through with it. I was going with this other girl, Barbara. We're in love. I had nothing whatever to do with the crime. All right. What was Charlie to Eileen? He was in love with her. He came to my apartment tonight. Told me he'd killed her. He asked me for money to get aboard a boat. I gave it to him to save my own life. I saw he was desperate. Then I called you. That'd be all? That'd be all for Charlie. You see, I told him the absolute truth. I'm that kind of a guy, Charlie. Now if you want to kill a man for telling the truth, that's perfectly all right with me. But before you pull any triggers, try to remember my testimony in court. That was the truth, too. You remember, Charlie, I tried my best for you. Mr. Disco, will you tell the court what your relationship was with Miss Eileen Bishop? I certainly will be more than happy to. It was love. I loved her. She loved me. It was that simple. But things like that break up. You made love to her when she was engaged to the defendant? She made love to me. But you acceded to her advances. Mr. Bjornsson, Eileen was a very lovely girl. But if for one moment I had even one inkling that she loved Charlie, the defendant, never for a moment would I have considered forcing myself into such a relationship. Mr.  A pitchman. I sell gadgets at Coney Island.  I applied my profession since I was a boy. My father was a pitchman. Did you ever sell the defendant anything? No, sir. I don't sell merchandise to friends. On the contrary, Mr. Disco, you sold the defendant the biggest bill of goods of your life. That will be all. When they sentenced you to life imprisonment, I smiled. Yes, Charlie, I was happy. I was happy because I felt maybe I had something to do with the leniency of the court. Maybe because the jury thought I'd prodded you into a murder, which, of course, was totally untrue, as you know. Maybe by being a villain I'd made things a little better for you. And then what do you do? Instead of making things easy for yourself, instead of being thankful for your good luck, you negotiate a break and, boom, you're out of jail. Charlie, when I heard about that jailbreak, my heart hit the bottom of my stomach. I can't tell you how I felt. I thought you'd gone crazy while you had. What are you going to do, Nat? I've got to get out of town, Barbara, who'll be after me first thing. He knows he'll never get away with it. He wants only one thing to get me. I can call for reservations. We can leave on the next plane. Yeah, yeah, that's the best thing to do. Get out of here till I get him again. I don't know what I'd do if anything happened to you, Nat. Ah, you're wonderful, honey. You get packed. I'll phone for the tickets. No, no, I've got a better idea. Carr, we'll be free to go places. Whatever you say, Nat. Please, let's hurry. I was hoping so hard for you, Charlie. You'll never know.  And I felt bad enough about the whole thing, let alone have my death be the cause of yours. What is revenge? A moment, and then the suffering begins. So Barbara and I left for the South. We got as far as South Carolina near Charleston when Barbara told me the news. I just, just heard it on the radio, Nat. They got him. They did. In New York City. Just picked him up. Darling, we're safe. Yeah. Boy, that's a big relief. I was really scared there for a while. It's all over now, honey. Yeah. We can go back home. That's right. It's all over.  Feels good to be back, huh? Feels wonderful. Come here. Oh, baby, what would I do without you? Let it ring. Might be important. Yeah. Yeah? Oh, yes. Yes, Lieutenant. Well, I got a promotion. The last time it was Sergeant. Is the same one that was there last time? There this time? Well, I'm glad you got him, Lieutenant. It's just it, baby. I was just wondering if you were still in town. No, no, I'm back now that everything's all right again. Honey, sweetheart, if I was really the Lieutenant, I'd tell you that Charlie is still on the loose and liable to show up at your place any minute. What? That's right.  Bye, sweetheart. So long, Lieutenant, and thanks for the information. All right. What a big idea. What? He's loose. He's still loose. What's a big idea? No! Stay away from me. You want to get me killed, don't you? Sure, he's loose.  Right here. That's a sweet trick, getting me back to town, back to the apartment. How many other lieutenants have you talked to lately? That was Lieutenant's day. Stop it, stop it! I could hear her voice cracking all the way over here. But once you're not going to talk yourself out of anything, Nat, Charlie's going to be here soon. I'm going to call the police. Too late, Nat. You left town. The police didn't have anything to protect you or gone. This place was empty, remember? Go on, Nat. Talk. Talk loud and fast. You're going to need every word. I'm getting out of here. You're going to wait here till he comes. I don't mind waiting.  Smooth, fast talk.  You broke me, Nat.  Get out of my way! He's running up the stairs. Hear him, Nat? Out of my way! Talk, talk, talk yourself out the back way. Go on, Nat. Talk. Charlie!  Get out of here. You didn't get out of town like I expected, Nat. You just sat up here waiting. All right? Make you a pitch. I got time. So, there are your reasons, Charlie. You see, I've told you the truth to the best of my ability. So, you see, that's the case I present to you for your inspection. Listen. Listen, they're outside. The police, they're here. Okay. Shoot me and get the chair. Or else, here's my offer, Charlie. Come with me and I'll help you get away. I've never stopped being your friend, Charlie, despite how you might have felt about me. I've got some money, too. Not much, but some. And I'm sure, Charlie, with my connections, we could get you out of the country. I've never lost faith in you, Charlie. And even now, during your present difficulties, I still haven't lost faith. That's friendship, Charlie.  Because, Charlie, you can shoot me down dead.   Loving you with my dying breath. You're through, pitchman? Yes, Charlie. I'm through. No dice. Suspense. Presented by AutoLite, tonight's star, Mr. Richard Widmark. Friends, this is Harlow Wilcox again to remind you that AutoLite is the world's largest independent manufacturer of automotive electrical equipment. In 28 plants from coast to coast, AutoLite makes over 400 products for cars, trucks, planes, and boats, including famous AutoLite Stay Full batteries carried by your neighborhood AutoLite battery dealer. See him soon and ask for an AutoLite Stay Full battery, the battery that needs water only three times a year in normal car use. And remember, you're always right with AutoLite. Next week on Suspense, a story suggested by actual events and starring Mr. Gregory Peck, who will tell you the truth about Jerry Baxter. Presented on Suspense. Suspense is produced and directed by Elliott Lewis with music composed by Lucian Moraweck and conducted by Lud Bluskin. Tell You Why I Shouldn't Die was written for Suspense by David Ellis. In tonight's play, Hi Everback was heard as Charlie, Kathy Lewis as Barbara, and Joy Terry as Eileen. Featured in the cast were Larry Thor, Joseph Kearns, and Mary Ship. Our thanks to 20th Century Fox Studios who made possible Richard Widmark's appearance tonight. Watch for Mr. Widmark in that studio's forthcoming production, The Frogmen. And remember, next week on Suspense, Mr. Gregory Peck in a tale we call The Truth About Jerry Baxter. You can buy AutoLite Stay Full batteries, AutoLite standard or resistor type spark plugs, AutoLite electrical parts at your neighborhood AutoLite dealers. Switch to AutoLite. Good night. Today, many physically handicapped persons are performing important jobs in almost all fields. If you're an employer, why not check with your state employment service? Perhaps your employment problems can be solved by physically handicapped but skilled and capable workers. This is CBS, the Columbia Broadcasting System.


Hello everybody Andrea here with dental L. So I've been in the dental profession now for about 17 years and I currently have my own mobile dental hygiene practice and I offer teeth whitening. So I go into patients homes and I do dental hygiene services and offer teeth whitening as well. But I remember those days working in an office so I've only had my own business since 2018 but prior to that I worked in a dental office I worked in several. I have moved a few times so I had to work in different dental offices each time and I also you know every office is different and I would also train new assistants new hygienists and I really got to see what makes a really good dental hygienist so it doesn't matter if you're brand new or if you're not brand new. There are certain qualities that stand out that make a really good dental hygienist so there is a course now where I help newly graduated dental hygienists kind of give you guys a rundown of how a dental office works. You can't be perfect and no dental office expects you to be perfect right away it can take years to really feel like you get a good grasp on things completely. But I remember being a new dental assistant and new dental hygienists and I remember thinking I wish there was a booklet that I could just read to prepare me for working in the dental office because I don't know where to start. If you've never worked in a dental office before it's very overwhelming how can it not be you're seeing real patients real people who don't want you to make mistakes they don't want you to not know what you're doing. And if you act like you don't know what you're doing you're going to make them uncomfortable so I have a course that gives you everything you need to know for working in a dental office I talked about infection control. I talked about how I talked about the basics of how to manage sterilization so you know how to do that if you can help if you have downtime if you have a no show. I talked about how you can help certain members of the team staff when you're not doing anything so you're not just sitting there twiddling your thumb so then when you need help one day that staff member is going to help you. And importantly though I teach you guys how to manage the patient chart, so you don't have this new patient chart looking at you, and you go, Okay, what am I seeing them for.  The patient asks me questions, what do I do, I teach you guys how to look in the chart, and how to go to the last few entries to really prepare yourself for that appointment. I remember being in a new dental hygienist and really struggling with what do I tell the patient do they come back in three months do they come back in six months do they come back in nine months. Sometimes it's not as easy as okay this patient has been coming in for nine months for the past 10 years, we're going to keep it like that what if you see a new patient. What do you do where do you start do you do the new patient exam does the dentist do the new patient exam. What about a full probe, do you ask an assistant to come in to help you or should you be able to do it yourself. I teach you guys all of these things I teach you guys what makes a good dental hygiene treatment chart note. How often you should be doing the full perio probing how to talk about perio gingivitis I give you guys templates if you use a digital computer software in your office. You can copy and paste that template to make it so much easier for you so you don't forget anything or at the very least print out that template. Look at it as you're making notes in your new office so you don't miss anything. I teach you guys all of that. I also go through things that people don't necessarily talk about but they really should, and that is dealing with difficult patients. How do you deal with the patient who says to you, I've never seen you before I want the other girl.  When I first started off in the dental profession I was 19, and I would have patients actually say to me, I don't want her it kind of looks like she just got out of school. I did, but I'm excited to work you know so how do you deal with those patients. How do you deal with difficult staff members I talk about that is as as well. Not all staff members are going to be happy that you're new and that you're working there. Some staff members are just mad all the time, all day long so you being a new person isn't going to make it any different. I don't know how you can talk to the dentist, how you can ask questions how you can feel comfortable and act like a pro, even if you're not a pro. So I go through all of that with you to. I talk about dealing with adult patients, seniors, children. So guess what you guys I go through everything you need to know to be a new dental hygienist in the office I literally go down to the basics. You know, Andrea, it's my first day on the job. When should I show up should I call the office and ask them if there's a uniform or do I just assume there's a uniform. Do I stay late to help other staff members, what if I'm half an hour behind all day, what do I do. Does the office expect me to be on time since I'm a new dental hygienist, I go through all of that with you guys so just a quick sneak peek. I want to show you guys inside the course. It's currently being updated so there will be more inside the course which is super exciting, but just to show you guys so it is a video course. So, there are some PowerPoints as well to read through things but primarily it's me talking to teaching you so you don't have to sit down and just read something because that's boring. This is more exciting but but if you guys look look under all of the modules. I talk about everything you need to know. I talked about real life real life as a dental hygienist I talked about loops, calling and sick. What if you have 30 minutes to clean the teeth what if you have half an hour, half an hour 30 minutes what if you have half an hour what if, if you have 45 minutes what if you have an hour. Do you hand scale, do you use the piezo or cavatron. I talk about different computer softwares I talk about perio, how to explain perio to your new patient. I've literally talked to you guys about everything and the nice thing is you guys inside the course. If you have questions you have my full contact info to reach out to me anytime so you don't have to be nervous, starting your new dental office so let me know you guys if you have any questions I'll leave the link for you down below. I am here to help new dental hygienists, I love it. And let me know if you guys need anything click like if you liked this video, and I'll talk to you guys very very soon.


The climate crisis can feel overwhelming. We get it. But at EESI, we also get what needs to be done. And we're doing it. We're working with Congress to implement pragmatic environmental policies. And we're on the ground to help families and businesses switch to clean and efficient energy solutions. Realistic solutions like renewable energy, large-scale rain gardens, energy efficient buildings, and much more. Realistic solutions that you can make possible.  Your donation to EESI makes you part of the climate solution. And it's money well spent. Don't just worry about the climate crisis. Do something about it. Consider it your gift to Mother Earth and make a world of difference.


Hello, welcome to NPTEL NOC introductory course on points at topology part 2, module 41 dimension of subspaces and unions today. Take a subspace of x, say x prime. Let us have this notation boundary, I read it as a boundary prime inside boundary inside x prime. Do you know what the boundary of a subset with respect to x and x prime respectively. Then for any a inside x, we have the boundary of a intersection x prime taken inside x prime. That is a subset of boundary of a. Without any decoration, this boundary just denotes the boundary inside the larger space x. So, this is an elementary result which you have seen in the first part itself, but now it becomes very crucial.  Take a point which is the boundary of a intersection x prime in the subspace x prime. Let us start with that. a can open set u of x now such that x is inside u. We know that u intersection x prime is a neighborhood of x in x prime and hence u intersection x prime intersects both a intersection x prime and its complement inside x prime because it is a boundary point of intersection x prime. Therefore, this u intersection a which is the union of u intersection x prime and a intersection x prime this has to be non-empty. So, we have proved that starting with any open neighborhood of x, u intersection a is non-empty. What else we have to prove? We have to prove that its complement also intersects u. Then it would be a boundary point of a intersection x prime a itself inside x. So, what is the intersection of u with x minus a that contains u intersection x prime as well as complement of a inside x prime. So, those which are x prime inside x prime those which are not inside x prime I have taken entire u intersection x prime. But the first part is u intersection x prime. The second part is x prime minus a intersection x prime. So, one of them has to be non-empty as we have seen. Therefore, it follows that x must be inside boundary of a. So, one way is true. In fact, equality hardly occurs unless a itself is a close subset of a intersection x prime is a close subset of x prime or x prime itself is close and so on. So, all that we need is one way in equilibrium here. So, we will use this one heavily now. Every subspace of a space of dimension less than or equal to n is of dimension less than or equal to n. When you take subspaces dimension does not increase. So, this is the theorem here now. So, start with a base for x such that dimension of the boundary of each member is less than or equal to n minus 1. So, that is the definition of dimension being less than or equal to n. Then we know that if you take b prime namely b intersection x prime as b ways over b that family is a base for x prime because subspace to power dimension. By the lemma we have boundary of b intersection x prime inside x prime is contained inside boundary of b. Now, we induct on n. If n is 0 this implies the boundary of b is empty. Therefore, for each b inside b therefore, this is also empty. So, this proves a statement for theorem of the theorem for n equal to 0. Inductively assume that we have proved the statement for n minus 1. Now, this implies boundary the dimension of boundary of b intersection x prime is less than or equal to n minus 1 because it is subspace of the corresponding here. Hence dimension of x prime is less than or equal to n. So, all the time we are using this one. If the dimension is say 5 here that will be dimension will be less than or equal to 5. Once we have proved that for a for 6th dimension it will prove and so on. Starting with 0 you can build up the induction. Next theorem is that x be a subspace of a separable metric space any space for that matter and separable metric space you start with. Then x as dimension less than or equal to n you spend only if given any closed subspace c of x and a point p inside p not inside c outside c.  Remember if remember what is s2, s2 said that points can be separated our closed set and a point can be separated by closed sets. Closed sets where those with such that dimension of the boundary sorry the boundary itself is empty. Now here we have something else this is extended s2 it is n minus n dimensional s version of s2. So, dimension of x less than or equal to n you cannot expect closed sets and a point outside it could be separated by closed sets. Closed sets means boundary is empty. Now on that boundary we are going to put condition so this is elaborately stated in a different way here you throw away closed subset d of dimension n minus 1. Then you have a separation when you have a closed set the boundary played that role that is why we did not have to bother about this way stating. Now here we throw away some closed subset of course away from c and p p and c you have to retain. So, x minus d is a union b a and b are both closed and both open inside x minus d and p is inside a and c is inside b all the other way around. So, this is the generalized version of s2 now you see. So, this is equivalent to having dimension n just like s2 is equivalent to having dimension 0. Let us prove this one. Suppose x has dimension less than or equal to n with c and p as stated means closed subset and a point outside take the neighborhood u which is complement of c. So, that is the neighborhood of x by regularity of x because x is several matrix based off rule. We get an open set v in x such that p is inside v closure of v is inside complement of c because p is inside complement of c and complement of c is open in between we have got this v and v bar. Since dimension is less than or equal to n we get an open set w inside this v p belonging to w is contained inside v such that now you take d what is d? d I have to choose namely boundary of w is of dimension less than or equal to n minus 1. So, this is the statement for dimension I mean condition for dimension being less than or equal to n. Now, look at x minus d d is a boundary of something so it is a closed subset. So, x minus d is obviously union of w and x minus w bar both of them are open union is this one. So, both of them are closed in x minus d p is inside w and c is inside x minus w bar because of what? The boundary of w bar does not intersect in p. v bar is contained inside a complement of c and w is contained inside v. So, w bar is also contained inside v bar. So, c is contained inside x minus w bar. Conversely starting with any point in x and an open subset u such that p is inside u put c equal to complement of serious time.  This implies a is an open subset of x because d is a closed subset. So, a is open inside x minus d and d is closed out x minus d is open inside x. So, a is open subset of x p is inside a a is contained inside u because it is disjoint from this c that is all. Also boundary of a will be contained inside d and hence of dimension less than or equal to n minus 1. So, what we have done starting with any point and an open set we have produced a neighborhood such that its boundary is of dimension less than or equal to n minus 1. So, this just means that for every point we have done. So, we have a base for x consisting of elements a such that their boundaries are less than or equal dimension n minus 1. So, that means that dimension of x is less than or equal to n. Now, it is convenient and useful to express the condition for a subspace x prime of a space to have dimension less than or equal to n purely in terms of you know condition on larger space x. We know what is the condition subspace there is a base for subspace with water blah blah blah satisfying. So, we can say that generalized S2 condition. So, let us convert that purely in terms of x that will be useful for us. So, this lemma says start with a metric space is general lemma. Let x prime be a subspace suppose a and b are subsets of x prime which are mutually separated in x prime remember mutually separated means a intersection closure of b is empty similarly b intersection closure of a is empty. This time I am taking closures prime inside x prime because there are two spaces in all here you do not know where you are taking if you just say closure or b bar and so on. I will use bar to denote the closures inside x the standard one for subspaces I will use this notation closure prime. Then there exists open subsets w in x such that a is contained inside w, w bar intersection b is empty. So, this is again a general result while proving a studying metric space is we have seen such proof but let me recall it because now it is become crucial. All that I have to do is use the metric property by the way this is general just about any metric space. So, put w a equal to union of all open bars b r a where a range is inside a and one condition on r namely 3 times r b 3 times r a ball of radius 3 r around a does not intersection b. So, points of this you know a must be far away from this one 3 times r m should be there this must be empty of course, r should be positive. This is just the definition w a is union of all such balls similarly w b is union of b r b b range over a same condition now a and b interchange b 3 r b intersection a is empty. Then clearly both w and w b are open subsets of x because they are unions of open balls. It suffices to show that a is inside w a w a intersection w b is empty because b is inside w b and that is open automatically it will imply w a bar intersection b is empty. So, after that you can take w equal to this w a we want w to be an open set containing a such that its closure in x does not intersect b. A set does not intersect in open neighborhood around a set will not intersect its closure will not intersect that set that is all. So, let us prove that a is inside w a and this one inside this one provided see we have not yet stated. So, what is the hypothesis? Hypothesis is a and b are separated mutually separated we have not used that one yet. The basic observation we make here is that if d prime is the metric d restricted to x prime the same metric but points are taken inside x prime that is the meaning. Then for all x prime inside x prime b prime t x prime this is a definition t is the radius x prime is the center that of all y prime in x prime such that d prime of y prime x prime is less than t nothing but the standard ball in x around x prime and points inside x prime I am just repeating the meaning of what is the restricted metric here let us know all that. Now, a intersection closure of b inside x prime is empty implies see these two are a and closure there exists some point r positive such that the ball of radius 3 a of course this prime I am taking only everything working inside x prime now intersection b is empty. But then b 3 I am talking about one point here for each a b 3 a intersection b is b 3 r a intersection x prime b because see these things are a and b are inside x after x prime after all this ball is outside inside x if you instead b b is x prime intersection b I can once you have x prime this is nothing b b prime of 3 r a b prime 3 r a intersection b is empty. So, for each a if you choose r like this then what you have what is that point and this neighbor is inside this so this proves that when you take the union a is contained inside w a argument is similar because a and b have been interchanged in defining w b so b is also contained inside w b alright. Now, you have to prove that w a intersection w b is empty and that is why why we are taking only balls of radius r but condition is on on the ball of now 3 times larger that b 3 r so that the triangle inequality will help you that is all here the standard triangle inequality you have to show suppose your point which is in both w a and w b okay that implies this x this x is inside some b r a as well as b s b for r and s some positive number right and a and b are inside a and b respectively but then distance between a and b a to x and then x to b will be less than r plus s okay triangle inequality here b 3 r a intersection b is empty this implies r plus s must be bigger than 3 r right because the ball of 3 r a it doesn't intersect this so r plus s must be bigger than this one okay that is what is the meaning of this one consulate one s is bigger than 2 r similarly b 3 s b intersection a is empty that is the choice of this s and r after all that will imply r process is bigger than 3 s okay but now s is bigger than 2 r so r is bigger than 2 s right so s is bigger than 2 r r is bigger than 2 s there is a and there are different ways of getting contradiction once you know that the triangle inequality has to be used here okay now let us go to the zero-dimensional dimension theory let x prime contain inside x now I am working with a separable metric basis okay then x prime has dimension less than go to n if and only if x prime okay for every point p belonging to x there exists arbitrary small neighbourhoods w of p in x I want everything inside x now okay such that dimension of this w boundary of w is also taken inside i intersected with x prime is less than or n minus okay that is as far as you can go everything trying to do only in terms of x it is not possible somewhere you have to you have to involve x prime and that is involved only at the last moment you have a neighbourhood of point neighbourhood of that point for every point okay inside arbitrary small neighbourhood of that point such that you look at the boundary of that inside x now you intersect with x prime dimension of that much less than or n minus okay everything if you do not worry about going to x at all inside x prime that is true from that I have to get a neighbourhood w of this point inside x with this property so that is the gist of the theorem okay and the converse converse is obvious here anyway assume that the given condition is satisfied that is part is converse part here that p belong to x prime and u be a neighbourhood of p in x prime now every neighbourhood can be expanded to a neighbourhood of of the point inside the larger space right by definition of subspace to power h let u be a neighbourhood of p in x such that u prime is u intersection x prime then by the given condition you have a smaller neighbourhood w of p such that w is contained inside u and dimension of w intersection x prime is of dimension less than or n minus 1 this is the stated condition in the theorem now you take v prime equipped w intersection x prime then u prime is contained inside v prime and we know that the boundary of v prime inside x prime is contained inside boundary of w intersection x prime so this lemma we are using it again here which is given to be of dimension less than or n minus 1 okay so now we can conclude by theorem 9.2 9.2 value that the dimension of x prime is less than or equal to n minus 2 n okay converse suppose dimension of x prime is less than or equal to n given a point p inside x prime and a neighbourhood open subset in the larger space x such that p is inside u there exist an open subset p inside x such that p inside v prime which is v intersection x prime contained inside u prime which is u intersection x prime and dimension of this v prime that boundary of this v prime in x prime has dimension less than or to n minus 1 okay this is the meaning of dimension of x prime is less than or equal to n starting with an arbitrary neighborhood u inside that I can find a neighborhood v prime with this property because dimension of x prime is less than or to n okay the boundary of this x prime is taken inside this one you recall that this is nothing but closure inside v prime to closure inside x prime of v prime minus v prime which is same thing as you subtract v does not matter that is the meaning of this one all right now recall that if a is an open set in a topological space y and b is y minus a bar then a and b will disjoint open sets they are mutually separated inside y okay start with an open subset and take b to y minus a bar automatically boundary of you know a and b are themselves are disjoint open subset and the union will be so they are separated by boundary of you but it is in the whole here applying this with y could x prime a equal to v prime and b equal to x prime minus the closure of v prime closure taken inside x prime okay this general statement I am applying it for y could x prime now start with a open subset a which is v prime and b I am taking the complement of its closure closure of a here we conclude that this a and b are mutually separated in x prime therefore by the above lemma previous lemma we get an open subset w of x as that v prime is inside w closure of w intersection x prime minus the closure of this one that is b is empty so this is b I have taken therefore w bar intersection x prime if you take the only in this intersection that must be contained inside this subset which you have thrown away once throw away this one it is empty so this must be contained inside closure of v prime inside x prime okay we also have v prime is in fact contained here w now okay it started with such a thing and hence v itself equal to v prime intersection x prime all right that is how we started with v being a neighborhood of v being an open subset of x here v prime to say that is contained w intersection x prime so putting these two together what we have is boundary of w intersection x prime will be boundary of w by definition w bar minus w intersection x prime which is w bar intersection x prime minus points of w have to be thrown away w intersection x prime okay but this is nothing but the closure of this is contained is a closure of v prime and that is a large this is a small subset of this one this is a larger subset this is subset of this one so this this is subset of this one because this is subset of this one this is subset of this one okay so but this is nothing but boundary of v prime taken inside x prime and that is precisely the statement in the corner spot we took some set theory set topology here you have to do it carefully now we have a beautiful theorem here not very beautiful because you may expect that dimension of the union is equal dimension of a plus dimension of v however such sweeping things are not work so slight modification is necessary yet it is quite beautiful that is what I want to say a and b are subsets of a separable metric space no other condition then dimension of the union is less than or equal to dimension of a plus dimension of v plus 1 okay only thing is they should be defined in the sense that if one of them is infinite suppose this is infinite then a dimension of a is infinite then this is less than equal to infinite is obvious if this is infinite one of them will be infinite so some such things are there I want to avoid all that I want to take case where in dimension of a plus b is finite dimension of a is finite dimension of b is finite okay you can examine when what happens when they are infinite and so on no problem you see when you are writing inequality here you have to be careful about something being infinite and if this is infinite and this is finally no problem if this is infinite this means that one of them here must be infinite okay I am not covering that case here okay let us do induction induction can work for finite case only right or the sum dimension of a plus dimension of b the least value of dimension of a plus dimension of v both of them empty is minus 2 right and then if both are empty it is also empty okay minus 2 plus 1 is minus 1 so this is okay you see even at the even at that level empty set empty set okay dimension of a and b is empty is less than or equal to minus 1 minus 1 then you would have won't have made sense right see minus 1 is not less than equal to minus 1 plus minus 1 so you have to add one more even at that level this plus 1 is necessary there okay even at the very beginning all right so this case is over the least case all right now assume dimension of a plus b dimension of a plus dimension of b greater than or equal to minus 1 it just means that at least one of a or b must be non-empty that is all okay suppose a statement is true for all pairs of spaces a prime b prime whenever this happens namely for which dimension of a prime plus dimension of b prime is less than dimension of a plus dimension of b this is the induction or induction hypothesis here not just for a and b okay whenever see this is some number which is bigger than equal to minus 1 for numbers which are smaller than this namely sum total the induction is on this one right smaller than that the property should be true namely dimension of a prime even b prime should be less than or equal to 1 plus dimension of a prime plus dimension of b prime that is the induction hypothesis then we want to prove it for one higher namely first of all it follows that a union b is non-empty that is what I have told you already take p to be in the union okay b and u be a neighborhood of p by symmetry we may assume p is either in a or in b so you assume a just for writing down the proof by the previous theorem there exist a neighborhood v of p such that v is contained inside u and dimension of v intersection a is less than two dimension of a minus 1 the previous theorem enters here you see everything is happening inside x except the last condition then the dimension of w v you know daba v intersection a is of dimension let us go to this one okay so we also have dimension of boundary of v intersection b is less than dimension of b by because subspace is of this dimension here is just subspace okay therefore we can apply the induction to the pair boundary of v intersection a and boundary of v intersection b is by a prime b prime the sum total dimension is smaller than dimension of a plus dimension of b one is smaller strictly a minus 1 the other one is at least that much so sum total will be less than dimension of a plus dimension of b therefore induction hypothesis should be applicable to these two subspaces okay to conclude that the union of these two subspaces is less than required dimension less than equal to 1 plus dimension of the first one is a minus 1 dimension of a minus 1 here you see the other one is less than equal dimension of b okay so sum total 1 and 1 cancels for dimension of a plus dimension of b okay since this is true for every point p inside union from the previous theorem we conclude that dimension of the space namely a you know b must be 1 plus dimension of a plus dimension of b see this is for the boundary of the neighborhood so 1 plus will be 1 more with the dimension of the spaces so induction is quite easy here once you have this theorem which gives you you know in terms of the ambient space a in and b instead of I do not have to work with a by a and separate b separately the boundary of v is taken inside a and b now we have another easy corollary it is something funny here you can you can say union of n plus 1 subspace is of dimension 0 has dimension less than equal to n you can't say it's dimension 0 okay dimension when you take union may go up one at a time you have seen that in the previous you know we have seen that that is a statement of previous theorem so this is an easy corollary to the previous thing namely you know you take a two zero dimension spaces the union is less than equal to dimension 1 one take one more less than equal to 1 plus 1 and so on it goes on right so you will get dimension less than equal to n you know here is an example now start with any integer n possibly positive otherwise there won't be anything left here and take m to be smaller than that okay you can take equality also let m upper n lower m curly m upper m lower n denote the space of all points in R n at most m of whose coordinates are rational here you had or curly r m n earlier where exactly m coordinates were rational and so on now at most so you have to be very carefully here okay at most m of whose coordinates are rational and curly l l n m same n m denote the space of all points of in R n at least m of whose coordinates are right okay n is the total dimension R n this m denotes how many coordinates are rational and how many coordinates are rational here the first part is for m at most m of them are rational the second part is at most at least m of them are rational okay then dimension of curly m is less than equal to m dimension of curly l less than equal to l minus m okay how do you do that let us look at this space coordinates at most m of them are rational so you can start with R n 0 which is no coordinate is rational okay which is full all the all the coordinates are irrational this R n 0 we know that is 0 dimensional then R n 1 exactly one coordinate is at most at most at most m coordinates are rational right exactly one coordinate is rational that is also included here like that 1 2 3 up to m exactly now each of them we know we have studied they are 0 dimensional how many are there m plus 1 right so dimension is less than okay exactly similarly we have the other way around here here at least m times m of the coordinates are rational so take all the m of rational okay okay at least m of whose coordinates are rational R n m then R n m plus 1 okay one more one more how many all of them are in they are all again we have studied they are all 0 dimensional how many are there n minus m plus 1 right therefore the dimension total dimension is not in mind we will stop here we will continue again next time some theorems for n dimension spaces thank you


Very good morning. It is Wednesday, 17th of March. I hope you're doing well. Welcome to FMC Day. And ahead of that, things as you would anticipate, relatively quiet. A couple of things to update you on in terms of the clothes on Wall Street, an auction we had in the US last night, and then the age of pack session. In terms of the news flow today, talking a little bit of an update on the Astra vaccine situation. We'll have a look at France in particular, and then looking ahead to the FMC. And so starting off with the charts and how things reside this morning. We did close, slightly mixed on Wall Street, minor losses in the S&P and the Dow. The S&P down two tenths, the Dow down four tenths of one percent. So the S&P snapping those three consecutive record-breaking kind of sessions in a row. Energy and industrial sectors were a touch weaker. But Apple, Microsoft, Facebook, the big mega cap tech names helping lift the tech-oriented Nasdaq 100 to finish positive. So a little bit of divergence there as we're used to seeing on those day-to-day closes. So the Dow off its record high as well, but the Nasdaq finishing up around a half a percent. Overnight in Asia, relatively mixed. Nothing to really give us much of a head start here in the European Open. So the DAX down, but fractionally just blurs pivot in the futures here. You can see in the center left down just 18, so fairly marginal overall. Currency markets have been pretty quiet. Dollar index was basically unchanged just while going into this recording. And that's quite normal ahead of the Fed where you get kind of uncommitted trade as people kind of sit on their hands waiting to see what the power and his colleagues come out with. But just having a quick look at these major currency charts looking at Euro dollar here. Firstly, a significant level near term here going back to the ninth of the month where this has been a good marker of price activity on both below and above this price level at 1.19, 33.5 in the futures. Today as well you've got the pivot level pretty much sat at the same level about one or two pips just above that particular zone. So here near term, this would be a key area to look at and perhaps we get a bit of consolidation here just awaiting the announcement later on this evening. Don't forget as well if you're based in London, given the clock change, the FMC statement being at 6, the press coverage at 6.30 p.m., so an hour earlier than normal. I'll be covering that with the team. We'll do extended live streaming through the Discord channel for Amplify Live. But having a look then elsewhere at Cable. Cable just had a momentary breakout of just the Asia Pack range here. You can see that we tested yesterday afternoons high. The Asia Pack high just had a bit of a breakout. No fundamental headline that came out. More just technical down, a little bit of a run to the upside. So a marginally minor cable app performance against the Euro at the moment. A few people yesterday were observing that trend, sterling outperforming against the Euro in kind of relative terms. And yeah, you could take a look at the whole European handling over the Astra drug, although the composition of their drug basket, if you like, for the overall e-rollout, isn't as heavily geared to Astra as say it is in the UK. It's still obviously an important component to a more effective and speedy rollout of vaccines. And the disruptions that we continuously have been seeing with Europe on many different fronts, perhaps amplifies that divergence a little bit about where the UK-US is at the moment, comparative to where much of the mainland Europe is at this present point in time. We'll have a look at that in a moment because the other thing here is case rates are definitely picking up in mainland Europe now much more evident than they have been in recent weeks. And perhaps that's room for a little bit of reasoning rationale behind some of that recent divergence. Otherwise, elsewhere, just having a look at the S&P here. After breaking out yesterday, or not yesterday, day before evening, we've kind of used that breakout point as a bit of a platform now for price. We did momentarily break through there just after Europe exited the market yesterday as we kind of collapsed off all-time highs and a bit of short-term profit taking given the squeeze up that we had. So be looking for that to hold probably now just going into the Fed meeting later. Pretty similar price pattern developing in the NASDAQ. And then in terms of the US 10-year, a little bit of a breakdown in the kind of cleanness of the correlation of yield being a decent front indicator of subsequent movement in other asset classes. Yesterday we saw again a 10-year knocking on the ceiling of that key area around 130203 and an about turn then we've just drifted here as yields have just picked up a little bit. We'll talk about the Fed in a moment, but there is a few people chiefly led by a view coming out of the Chief Economist at Goldman Sachs looking for the median dot plots for the rate view of the FMC projections to be indicative of a rate hike in 2023. Albeit, I'd say that's not what the base case scenario is, which is for it to remain the same as it was effectively that the median hasn't had enough members shift to make a hike in 2023 but rather through after 2023. We'll talk about this more in a moment, but that 10-year level still very key of course and definitely is going to potentially be something to watch later on this evening. And again on the daily chart the rationale being this has been holding us up at these levels which has been very key because it does open up almost a trapdoor to a deeper move and a further acceleration perhaps of another pop on the yields to the upside if we were to break through under the right circumstances today and the catalyst of course could well be Powell and the Fed. So let's talk about the Astro news. Firstly, we have had France and Italy considering basically a U-turn on the Astro vaccine following comments that we had yesterday from the European Medicines Agency, the EMA, their duty of kind of give a more formalised response to this ongoing blood clot rationale that's led to many European nations suspending the Astro drug. But France and Italy have come out basically said that despite the EMA not issuing a definitive assessment they've repeatedly said the benefits of the shot outweigh the risks and so therefore these two countries have said they're willing to go with the medical advice and look to resume then the Astro drug. And the reason why this is quite important is because if you look at the COVID situation this isn't daily new confirmed COVID-19 cases per million on the rolling seven day average and if I hover over these countries here this is France at the moment and as you can see we've just popped up yesterday to the highest we've been here today and definitely over the course of the last couple of weeks or really going back to the last quarter really from the beginning of the year this number has been heading in the wrong direction it's been steadily creeping higher and what that's led to is France now is weighing implementing a weekend lockdown for Paris the French capital has been under a nightly curfew since mid-January with cafes, restaurants, bars and theatres all closed but as you've just seen infection rates have been climbing intensive care units in and around the capital are nearly full in a similar vein to what we were like in London and in the UK just a few months ago the other country here and of course the one that's commented about the U-turn on the Astro drug is seeing an equally challenging COVID situation as well at this present point in time which also has led to several regions having more stringent lockdowns put in place by the new caretaker government under Mario Draghi so you can see here Italy and France definitely being much more conscious of turning the decision of the vaccines and probably due to the circumstance that we're seeing here with COVID-19 the other country of course Germany and if you look at Germany it's much lower level but that as well has been picking up so more so than what we're seeing definitely in the US which is kind of plateaued now after a very sharp deceleration in new cases and the UK same case as well so perhaps that as I said explains a little bit about that euro and sterling divergence the other thing we had overnight just to move away from this was we did have another successful bond auction in fact pretty decent one this was $24 billion auction of 20 year bonds which saw strong demand and of course this came after people were a little bit apprehensive given a really bad 7 year auction that we had back in February the $120 billion dollars worth of auctions 3 that we had last week went through OK that was a relief this auction was actually pretty decent so on that front I think those concerns have been alleviated in fixed income auctions I did specifically do an auction lecture video that I've put on the Amplifier Live portal because I had a lot of questions about what is a when issue and a bid to cover what is indirect primary dealers and these types of words what do they actually reflect what does it mean how to interpret this information so do check that out if you have any questions of where to find it just reach me in the discord chat alright well let's talk about the Fed and yeah good article in the FT just kind of summarizing things I will be on live later on tonight to go through this with everyone in full on Amplifier Live but the main things we're looking at here just to summarize are a few for one better growth but how much better I guess that's a good question and that's because this isn't about policy change as far as rates and QE are concerned the rates will be on hold the QE program 120 billion dollars worth of purchases per month 80 billion treasuries 40 billion MBS will remain as it is we are going to see the summary of economic projections and these come out every alternate meeting so typically March then June set deck and obviously this being the March meeting we haven't seen these projections since December so it's a good way for the market to see how much the Fed's view has altered since where we were in December to where we are now if you think about where we are now we've had a new stimulus gone through the 1.9 trillion for Biden just recently we've also had a drop in covid cases further reopening the US a faster pace with the vaccination rollouts these are all positive things so we are looking for a slightly more optimistic then view about where we are now to where we were then so subsequently in terms of things like unemployment likely to be revised then lower so more positive situation growth in inflation both higher explaining then tied to this idea and view of more firmer growth sooner so those things I don't think are going to be particularly shocking neither do I think they are going to be particularly market moving the one the market probably will latch on to of course is the idea of what is the median dot plot for rates and kind of triggered a little bit by a comment I saw from Yen Hacias who is the Goldman's chief economist yesterday he was talking about the idea that he sees a couple of these Fed members shifting to bringing forward a rate hike into 2023 enough of them shifting in order to move the median dot plot to rate high extend from a Fed official communication from beyond 2023 to in 2023 for one rate hike to materialize that probably be seen as hawkish in terms of how markets price at the moment I'd say most people me myself included I'm not expecting that actually to materialize that the Fed will stick or there won't be enough of the Fed members switching to move the median dot plot but probably if there is one thing you are looking out for at the point of release it's going to be that one comment for the first rate hike from the Fed in 2023 after 2023 I think if you get after 2023 a reiteration of what their current guidance is you might see a little bit of a relief kind of dovish response in that sense because there's a little bit of pricing for something a little bit more hawkish than that so what would that look like well maybe a bit of dollar softness lifting the major pairs might probably equity positive in that sense and then yields would move lower consequently then the T-note might move up again under those conditions what else is there beyond that point then what will the dots say well this is what we've just discussed have treasury yields risen too far too fast again this is that whole idea about what we've been seeing that's been destabilizing to a certain extent over recent weeks is he going to comment on this I really don't think he will I think he'll just kind of reiterate what he said before which I've got it written down the exact comment phrase that he said but he's basically going to say that they're still a long way off getting to their targets in terms of on the employment and the inflation situation and so therefore kind of indirectly pushing back against this idea that the Fed feels threatened by this recent rise in yields something we talked about many times before and I think the markets moved on a little bit from having this kind of clear expectation of him saying something but in the press conference in itself I'm sure people are going to be pressing him on this particular point so as this FT article suggests investors will be watching for any signals from the Fed about his plans to manage a rising borrowing costs especially if it begins to jeopardize the economic recovery that's begun to take hold so yeah the kind of key summary here is tolerance for higher yields is what we're kind of looking for any kind of thresholds parameters around that but again details are probably going to be lacking at this point he's not going to be wanting to pre-commit are COVID era era capital concessions here to stay so back in April of last year so basically a year ago US regulators allowed lenders to exclude treasuries and cash reserves when calculating how additional capital they need to hold in order to encourage banks to extend credit to struggling businesses and consumers so as the market conditions and economy starts to pick up and normalize then a lot of these kind of emergency facilities are no longer required and definitely you don't want to just keep them in the system you want to kind of get back to normal so if anything if there is a disruptive event then you can redeploy these things and so is this that point where we start to see some of these tightened up a little bit and then the other thing is will the Fed make technical adjustments this is where basically the Fed might want to tweak slightly some interest rates to ensure its main policy rate stays within the middle of its target the federal funds banned of 0 to 0.25% so yeah that's pretty much it overall definitely I think it will be a tradeable event I think there are some key things to look out for here particularly on the placement of where the dot plots would show the first rate hike coming from the Federal Reserve I think POW will manage the press conference absolutely fine and not cause too much of a disruptive event beyond that and overall I definitely think that it's going to be the period that we're going into not so much this meeting that's going to be really crucial then and a crucial test for the Fed and its tolerance for yields and its perception about inflation and how in control of that they can be and then ultimately how quickly the economy start to grow again as we start to reopen more aggressively in the US and what does that mean then for them to start to eventually comment more about the nod to tapering in the future time wise for that then I think the June meeting which is the next update for projections is way more kind of interesting at that particular juncture at that point we should have had most if not all of the people in the US are not calculated at that point the economy would have moved on a positive fashion all things being equal and then it's going to be a little bit more testing then for Fed to give us a little bit more clarity about what the future holds and again they're going to hint towards these type of ideas of tapering before it might start to commence towards the back end of the year perhaps in small increments winding that kind of up as the program kind of slows before then the rate rise coming in 2023 perhaps so yeah that's give it a bit of context from the top level but I'll leave it at that let you guys get on with the day again I think just to be kind of rational about what the morning might offer you from a trade opportunity a lot of people will be awaiting that Fed event and of course that's not until 6pm later on today ok take care guys and good luck