Ie, Sean. You said your team-meeting has gone well. Three wins out of five in all competition. Must be a pretty good week so far? I think we've been building on early season performances but changing that to get results. The details I spoke about, both ends of the pitch, are improving. The will, the demand has been obvious I think from the players to make sure that we do improve in them metrics and take our chances and be solid at the other end. Felly mae'r gweithio gweithio, ac yn ystafell, rwy'n meddwl yn y tro cyntaf, a'r meddwl yn ei gael ar gyfer gael, yn ein gwneud ym mhwyslwch. O'r ymgyrchol ar hynny, mynd i'w gwneud o'r 20% iawn? Oni ddim yn ei wneud, o'r cyfrifesio cyfrifesio a'r cyfrifesio yn amlwg, sy'n mynd i'w gwneud? Nid yw gweithi'n gwneud, mae'r gwneud yn cael ei gwneud yn cael ei gwneud. Mae'n gweithio i'r gwneud yn cael eu gwneud, i'w bwysigio, Sword of the Wild demand the energy of the side and the commitment to basically let them, or sorry stop them and create many chances. They get a lucky break sometimes that happens, they're a very good side. I think we've seen a balance this season of the way that we can perform, we've seen games where we've dominated with the ball and the metrics with the ball. I spoke about that more early in the season XG, et cetera. It's pleasing for me as the manager to see different ways of affecting games because over a season in the Premier League I'm pretty experienced in it. Unless you're the superpowers, particularly historically over the last number of years in Man City, I think you have to flex and change. That's what I've learned about the Premier League and I think we're showing signs that we can do that and the players can do that. VAR, it seems a conversation that you can have every single week. I know there were some issues for you last week. Are we any nearer or further away, do you think, from the clarity process? Well, I think it's a tough call. They're altering it, they're changing it. Officials in general, they're trying to promote new officials, they're trying to get growth in the officials and how they can blend into the Premier League. It's not easy. It's not easy for the governing bodies to do that, not easy for the referees either. I've said for many years that the three highest demands on a match day are the two managers and the referee. Within that, I think there's just some things that we think commonsensically could be better and I think quicker. I think that's probably where we just get a little bit lost in it as managers and coaches and players and I think the fans as well. I spoke recently and I'm still a fan of it, I've got to be honest, because the margins are tight and they're very, very important. It's top-level sport and it's top-level outcomes and financially can be massive difference in football from big important decisions. I just spoke recently about there's always a rule for a rule and there seems to be a rule for every VR situation. When you could take all that away and just put more strength in the VR people and go, look, you know, we've had two this season, you know what they are, massive decisions that were clearly obvious to everyone in the stadium that didn't get corrected because of a certain reason why they're not allowed to correct them. For me, there should be an override if it's a bad decision, it's a bad decision to end off, don't need a rule to decide on a bad decision. They should go, right, that's it, that's a bad decision and change it. It's not as easy as I'm suggesting, I'm sure of that because everyone will have a different view but I think there's a more common-sensical way that it can work and I think they are trying to find that. On the other hand, the demand of it is quite obvious, you know, stories of our referees speak to the crowd and all this sort of stuff. You know, my personal and Avarnaw's referees go into the radar, allowed to do their job and they do it so well. We hardly notice them, not bring them to the fore, but that's only a personal opinion. I've got a lot of respect for referees because I think it's a hard job. Yeah, just on that, do you think the discourse at the moment, are we fair to referees because there's so much spotlight on them and you know it's such a difficult job? But that's the thing, I don't, you know, I can't understand the spotlight in the sense of, you could change that because, you know, this idea of I spoke after the Liverpool game, people running over to the screen and we all more or less know what the outcome is going to be. So it just adds more spotlight on it, take that away, make it quicker, make it more streamlined. Personally, I don't need to hear from the referee and the VR, I don't think the stadium needs to hear it. It's a decision it's made, we get on with it. You know, I think it's a hard job. I think I was hoping when the VR first came in, it was streamlined in every season it was and to a point when we all got used to it and it was pretty quick, it seems to recently have gone the other way. The demand gets higher and you know, even if in my opinion, this is purely my opinion, if we have every ability to speak to everyone in the stadium, everyone presupposes because they explained that they'd all agree. Of course they wouldn't agree. Football fans, see if they're all going to agree, they're still not going to agree. So therefore I just don't, I can't see that. I think allow them to go out the spotlight, do their jobs. I think they have a really tough task as referees. We ask a lot of them. So my personal belief is just help them, don't keep adding more level to it and layers to it. Just take that all away, make it all quiet and down and let them get on with their jobs. Finally, from me, back to the football, Crystal Palace away on Saturday. Does the team find it easier perhaps played away from home than home at the moment? No, I don't think so. I think the, I've spoken recently about this, the results changed that perception. I think the performance has been really strong at home. The results changed the whole feel of that. I think we've been, I think we've actually been strong often, home and away. There's been a few that have got away from us. We know that. Hopefully we've corrected some of them things. But no, Palace is good club, fantastic manager, Ray Lunar as well, people are holding absolute high regard. So I look forward to seeing them, but obviously all the respect goes out the window when the whistle blows. Sean, just picking up on that, can I ask you about your thoughts on Roy Hodgson? Because he seems to get better with age, doesn't he? He was retired a couple of times. I tell him every time I see him, I've been telling him like this weekend, what are you doing? I say, why are you doing this for? Come on, mate. You know what I mean? In a lovely way, you understand. Terrific fella, always been terrific. Me, when I was younger, coming through, whenever I met him, come across him. I know him a bit through some work and connections I've done with leaders in sport as well. He's always at them events, speaks very wisely. Ray Lunar, and he was my manager at Watford. I've always gone fantastic with Ray. He was a great golfer as well. I like a lot of what they are and what they do. Respect them, and that's without a shadow of a doubt, but they know and I know the whistle blows, as I said, and that all goes out the window forever along the referee plays. Afterwards, I hope to go and see him and have a chat. Is Roy ever given away any of those secrets? I don't think he works in that way. I really don't. I think he's quite open, sorry. I think he believes in what he's done. He's formed it over many, many years and many experiences. I think he sticks to how he works with players and how he believes in the game. And it's paid him back. It's served him very, very well. I think he's still going. I certainly won't be able to tell him that every time. I'm not going to be doing it if I'm not on your age, mate. But it's a marvel to the fact that he's still got the bug in the heart and desire to keep doing it. And Ray as well. What are your thoughts on Crystal Palace? Especially recently, because obviously, before last weekend, I think it was one win in six. They then win last weekend and the narrative changes to they've taken seven points from 15. Well, that's life in the Premier League. That's life for clubs who are not the superpowers. You have the ups and downs, the ins and outs. Good club, Roy's done a good job. You know, like all clubs, I think, of that kind of build. Like trying to find that blend. You know, a side that can play, a side that can fight, a side that can get points on the table. And it's a challenge. It's simple as that. So they've had a bit of an awkward spell. I think Roy spoke what seemingly I've seen the game on a screen, not live, but he spoke pretty honestly after the burning am. And he thought they didn't play that well, but they got the result. But sometimes what you have to do. And concentrating on Everton specifically for this one. Any changes in the team news for this one? No, a couple of knocks with Amadou and Jarrod's got a bit of a knock. But we're not expecting to see Mr Omdux had a bit of sickness, but they've all been on the grass today, so we're hopeful on them. Hopeful on them, Anna, coming back. Yeah, I think he should be. I say they've been on the grass, as we know, still see how that reacts tomorrow. But he's managed that well. He's done well to get through the games he did. Hopefully we've managed that well with him as well. And it's calm now. Thank you. Thanks, Rich. We'll go to Julia. Excuse me. In the under-21 game this week, Use of Committee, Lewis Dobbin, Jarrod, Jr. Shane was common, all featured in that. I guess the big one there is Shavers Coleman. He lasted over an hour. Is he in contention for this game? It's important these games because we want to stimulate the players to get back to full fitness, full sharpness. The games program can be awkward, ranging games. So it's a game that we felt they could get something from, particularly Seamus, of course. He's still come back to true fitness, but he's doing great. He's put a lot of effort into getting back to real fitness levels. He's desperate to get back involved. You can imagine and be around it. But he's been terrific since he's been back around the group. And that helps. Use of getting a goal and working very hard. Dobbo needed a game, playing well. Some good habits and I'm pleased for the young players to come through that. Another good sign of a group working hard to get a result. I saw your interview this week where you mentioned about Deli Alley, to have a conversation with you about how he understood what you wanted to do about direct play. I just wondered if he has been helping maybe in training while he can't play on a match day. And also, the fans will want me to ask, are we expecting him sooner rather than later? No, he's still got a bit of a way to go. But no, I wanted to try and keep him involved. I think he's in a good place as a person. I like the fact that he absorbs it. He's had some amazing experiences, don't forget. People sometimes do forget that, for still a relatively young player. And I was just chatting to him about it. I just said, you know, I just want to try and keep him involved in what we're trying to do with the group. It's hard when you're out for that long. It really is. He's been through a lot over that period as well. And he just brought something up that I thought was really important and shared it with the players and said, look, having a calmness conversation. And he described it very well about, you know, this idea of direct play pre-supposed. That means kicking the ball another bit. It doesn't. And he was on it, you know, straight away. He said, oh, I get exactly what you mean. You know, can you play forwards is a first thought. And he said, maybe the players need a bit more correct team with that. So I told the players at the conversation, you know, I will try and be open with the players and I want their feedback. I'm more than happy for him to question things and ask why is it where false. And he did that in a very, very good manner. And I just thought it was important to share it and share the belief having all the players when they do feedbacks. We do listen. Well, no, but he certainly had a lot of experiences. Might stand him in good stead later on in life if he decides to go down that route. Vitaly Bicolenko's form, you know, is winning a lot of praise right now. I just wondered what you made of his progress since you've arrived here and also how he's linking up with Dwight McNeill, now he's getting his fitness back. Yeah, I think that, you know, Miko finished last season injured, which is an idea I got injured earlier this season. It was an awkward spell of niggly injuries. He came through the international scene and come back here for fitter. And he's done very well. You know, as soon as I got it, I liked what I was seeing. I think there's still lots of development in him. He defends very well. He defends a very high level kind of modern controlled aggression. You know, he's good on his feet. He wants to defend, but not silly stuff. Just a way he competes. And I think it's growing all the time. I think he's really improving. I've really enjoyed his performances. And Abdelai Dacore has decided that in January he's going to stay here. He won't be part of the Africa Cup of Nations. What does that mean to you as a manager and what's been the reaction within the squad to that? Well, I've always been respectful of players on the international scene because I think it's valid. You know, it means a lot to them to do that and play for countries and their like. So I think in his case, he's old enough and wise enough to make decisions. You know, it's not something he needed to speak in depth to me about. And it was a decision that he's made. Thank you. Just a quick one, Sean. There's been speculation again about Ben Godfrey and his future.  Yeah, he's doing terrifically well for us. He's trained very well. He's staying sharp and ready. The hardest thing we've had lately is the games program to try and keep the players not quite playing starting in the first team trying to keep them game ready. But he looks after himself super fit fella and he's going along well and he's ready. Does there anything more you're looking for to get back into the side? Well, I think it's fair to say currently it's tough. I think the two centre halves are playing very, very well and most people are speaking outside of my opinion and decision. I think most people accept that. And sometimes the centre half I was, and it's tough because you want to play. But I think there's an honesty to most centre halves to look at someone and think they are playing well. I know they've got to sit tight and I think he doesn't know that. I think he's a very good player but he's looking at two centre halves but currently I'm very, very strong for. Thank you. Thanks. Any further questions on the goal post-action? Hi, Sean. Amadu anon has been in great form and he currently ranks fourth in the league for successful long goals with only Rodgri, Thiago Silva and Moises Caise ahead of him. He's currently averaging twice as many as last season. Rodgri, has he allowed to pass it long?  I can't see him, I should tell him off. What would you put the improvement down to from a technical standpoint? Because obviously he's been really strong defensively. Is it simply just the case of his second season in England he's more confident or maybe something he's worked on? I think he's maturing as a player. I think he's realised the defensive responsibly better. I think he's doing it better. I think he's seeing the game quicker which I've spoken endlessly about to him and shown him some clips. Him and Jimmy to be fair. He sees things a bit quicker. I spoke to Amadu and Jimmy about the importance of their positional sense whilst trying to allow them the freedom to play as well because they can both play. They're very good on the ball I think and I think there's more to come and then putting in the hard yards because the top midfield players historically have always covered the ground and I think he's improved without the mental aspect of just the literal basics of working really hard as a midfield player and like I say, you've got Ghana there and Duke slightly differently playing a more advanced role but there's a good group there I think of midfield players who can rub off on each other. What do you think his ceiling is? I think like any player you can go as hard as you want for as long as you want. I mean I look at Youngie and I look at Sheamus they're still working hard at their game I think the way that I've always worked is not about age, it's about desire it's about the will, it's about what you want from yourself and I think for the younger players the world of football is open to so I don't put any limits on them just keep improving, keep being hungry to improve all of the time, I think that's the message from me. Thank you.


What's good Josh, we're Ross back again with another video. So I'm gonna check out why CM Punk will return to WWE. This is a very interesting statement from WrestleMania. The rumors have been running rampant Survivor Series this year will be in Chicago people are Just talking about all the rumors of CM Punk being there He's having meetings with Vince and the board of directors and all this other stuff And we really don't know and it's very interesting to see if it does happen But we're gonna see what WrestleMania has to say about this But he maybe he believes strongly that CM Punk will be back in WWE only time will tell But appreciate all the love and support you guys for showing on the channel. Let's get right into this one Here's CM Punk coming back to WWE. Well, that is the million dollar question that everybody is asking There have been rumors upon rumors of WWE Not wanting CM Punk back in WWE or WWE really rolling out the red carpet for him Now many fans do believe that CM Punk will be back in WWE with many believing he'll return at this year's Survivor Series War games Which also takes place in Chicago. However, why is Punk returning to WWE though? Well, let's look at the reasons why WWE wants Punk back And why Punk is willing to give it a second chance despite his stormy exit from the promotion Join us now as we look at why WWE is bringing back CM Punk Be sure to subscribe and hit that notification bell for daily wrestling videos and follow us on Facebook for exclusive lists Also, check out our new website WrestleAmya.com Now bringing CM Punk back is a risky move for both WWE and Punk There's no shortage of bad blood between the two some wrestlers can't even stand Punk and well vice versa Despite this business is business and there are still some incredible opportunities for both parties as we're about to see money We'll do may grow which has every reason to believe it could get burnt bringing Punk back The straight-edge superstar left the WWE on bad terms and he had two incidents in AEW one which led to his termination But despite this risk the WWE must feel Punk's benefits outweigh his risks Let's examine why the WWE may see Punk's potential for helping it as number one WWE wants its fans to forget Roman Reigns. Well for now Roman Reigns is taking another long hiatus from WWE after crown jewel Which means they could benefit from something which gets the WWE universe talking Yeah, especially about something besides why Reigns is taking another extended hiatus Punk's return is bound to have fans talking and focusing on how things will play out on television Behind the scenes who will Punk want to wrestle does he have any acts to grind? Will he return as a baby face or return as a heel? There are many questions the WWE Hope the fans will be asking when they hear Punk's entrance theme play And that is a fair point if you have him that's a very big name whether people want to admit it or not People are gonna definitely tune in even more to see what the hell Punk has to say if the focus is not gonna be Roman Reigns As much we know he's gonna be gone for a while if the rumors are true So the focus is gonna be what seeing Punk is gonna do which really changes Everything that we think is gonna happen potentially at next year's WrestleMania It throws a lot of things in to disarray because you have LA night still one of the hottest guys in WWE like the hottest superstars in WWE right now J is Super mega over Cody Rose is super mega over Do you add you add? Uh Sami Zayn gotta put him in that category you add see him punk to the mix those are five different wrestlers that Legitimately could main event WrestleMania potentially so I don't know It's gonna be very interesting if that does happen that that brings a little bit more entry outside of just Wins Roman coming back wants to stick it to a w I never underestimate just how important it is for the WWE to stick it to a Oh, yeah WWE is crushing things in terms of ticket sales merchandise and ratings But as long as a w is in business the promotion isn't irritant to the WWE bringing punk back to WWE will give punk a chance to vent on AEW and if he can succeed the WWE can boast that they knew how to use him Well without any headaches he caused in AEW WWE wants to keep things fresh Now a common reason for not bringing punk back is that the WWE really doesn't need him Fans and pundits of question why the WWE needs him when it's doing so well commercially and truly the adage If it ain't broke don't fix it doesn't apply here because one of the elements of pro wrestling is to keep fans guessing and keep things fresh Granted both the WWE and AEW have too many stars and both promotions fall into the trap of bringing in wrestlers Only they have nothing for them to do However, what are the chances that see I'm punk will be sitting in catering? Like they they will have there's so many matches. There's so many feuds. You can bring back Francis said it himself. He doesn't like seeing punk in multiple interviews. You that's a feud right there Him and Cody, that's a few they have history and you know You know people are gonna want to see see I'm punk versus Roman Reigns cuz they Have history. There's so many great stories. You can tell here It is it's money-making matches. You can tell here easily We clearly as plans for him and if he's used right, he'll create fresh matchups in WWE both with former opponents and wrestlers He's never battled in the WWE. Yeah, of course WWE wants to make merchandise money CM Punk Yeah, there's another lucrative source of revenue merchandise fans love to support their favorite superstars by wearing their merchandise and punks WWE return will lead to plenty of swag for fans to buy See some better quality items over the last year or two. That is clothing that they're not embarrassed to wear in public Designs a factor in wrestling's overall popularity and the WWE should be able to move plenty of punk products WWE wants to boost WrestleMania. Yeah, WrestleMania is the WWE show of shows Which traditionally is meant that WWE does everything it can to make it a must-see event 2024 show is more important than ever as it will be the first major product under the TKO Holdings banner Mm-hmm. So the first WrestleMania where Triple H has complete control over creative At least if the reports of TKO Holdings area manual asking Vince to stay out of creative are accurate It's unlikely the WWE is going to do any hotshot booking such as Vince McMahon did at WrestleMania 38 when he booked the title Unification bout between WWE champion Brock Lesnar and undisputed champion Roman Reigns regardless of the long-term consequences Yeah, what the WWE will do is to make sure mania is full of hot programs high-quality matches and two nights to remember The better and the match featuring punk is a special attraction that fits the WrestleMania mold and WrestleMania 39 They did a bang-up job night one still was Fantastic night to not as good as night one, but there was some great stuff in night two overall WrestleMania this year This past year was quaint. So they have a lot to live up to and Boy, you have the roster to have one of the best WrestleMania's again You have the roster and if you ask him punk to that mix It adds some unpredictability, so I don't know man This is gonna be interesting see if that does play out what a punk Does punk have any reason to want to return to WWE besides a big payday punk left the WWE with a very bad taste in his mouth And he has been quiet about it and sharing his thoughts on the way he was treated or how the company is run So why would he want to return other than padding his bank account? Well, CM Punk wants to prove critics wrong Yeah, CM Punk had a golden opportunity to prove his critics wrong when he returned to AEW First he had the chance to show he still has skills to put on the high quality matches His fans remembered him for second he has a chance to prove he was a needle mover Yeah, while punk was somewhat successful in both areas some fans He lost a step on the war his presence didn't juice in AEW's numbers in the long run His accomplishments were overshadowed by his backstage problems Unfortunately has a chance to reconnect with his fans and show he still got it and he's still relevant Well, that doesn't mean he'll succeed, but this is a fantastic opportunity Particularly since the WWE is so hot right now. There's a new sheriff in town One of the benefits of a WWE return is that punk doesn't have to deal with Vince McMahon and creative Nope, although there have been different accounts of our Triple H views punk and punk has been outspoken in his criticism of Triple H He will likely do what's best for business and put aside any personal misgivings about punk Otherwise, it's hard to imagine trips wanting punk back or punk agreeing to be booked by someone with an axe to grind Yeah, I do think I do think Triple H will be more willing to put put the past behind because they've been documented They don't like each other that much either But I do think they will be able to put it aside and they'll they'll they'll make good business That's the difference between WWE and AEW They will put shit aside people in the back You will you rarely hear about it either, but they'll put it aside and know they'll make gold They'll make money. That's what it's all about making the most possible money Not letting your ego get in front of the money making that that's dumb No, put the egos aside make the best possible money or go home Simple as that Things for sure see and punk misses the spotlight never rule out wrestlers love for the spotlight something which has led to many wrestlers Returning whether they're too old or they vowed to never ever again By most accounts punk enjoyed his return to the ring in terms of wrestling and fans reaction There's no doubt the politics in other workplace related difficulties bothered him But then again punk has never seen one to suffer fools gladly But this doesn't mean he's lost his passion for wrestling and the WWE return has much potential Oh, yeah, see I'm punk once his WrestleMania main event and that right there how long punk will stay in WWE and that's it Simple I could see him Wanted to come back to get that WrestleMania main event whether it's night one or night two. I can see that I Mean we Cody came back and he got his WrestleMania main event in a fantastic match I think the decision was wrong. I would end it, but boy. Oh boy was that match great Was the lead-up great too That's what punk wants the main event Yeah, if you got punk on your roster And he's coming back from the AEW stuff He's main eventing wrestling. There's no way you don't have a main event night one or two We either in terms of contract length or whether you can stay in WWE without a meltdown that prompts a premature exit But he's likely gonna be around and least until mania This creates a huge opportunity for punk as he could finally headline WrestleMania a goal He was never able to attain during his previous WrestleMania was just one night punk's chances would be slim Yeah, mania being held over two nights Punk has a much better chance at headlining the showcase of the Immortals Lastly, see him punk has some fresh opponents super fresh opponents 10 to the spotlight. He's likely excited about the opportunity to wrestle opponents He's never worked with before in WWE. It's likely punk will revisit some past programs But fans are likely to see some fresh matchups, which on paper should please punk his opponent and Fucking see him punk Mrs. LA night them on the microphone going back to back and forth opera. Come on Fans that would be crazy. We're turning at Survivor Series And we believe it's already locked in and the WWE as well as punk have several reasons for making this a never-say-never Situation possible the WWE and punk's reasons may not play out as planned But this scenario should make for one of wrestling's most compelling situations in some time Let's not forget. Where is the best place for punk to actually return? Yeah Yeah, his hometown in Chicago Could you think of any more of a bigger pop in our opinion? It could be an even bigger pop than you received in AEW because a surprise will be so caught off guard Yeah, so if WWE wants to make those ratings go through the roof bring back CM Punk What would you guys think we'll see I know some of y'all feel like CM Punk is not the draw anymore I know some of y'all feel like we don't need them and you have every right to feel that way So I'm not here to tell you that your opinion is wrong on that You have every right to but I will say this If you hear his music hit a Survivor Series not gonna lie to you.  It is It was a crazy moment hearing Cody Rose theme song at WrestleMania a few years ago And we all kind of knew he was gonna be there, but it was still a surreal moment to see it happen it would be a bigger surreal moment to see this because This is one of those things where we never thought we would see him back in WWE ever again Especially with AEW being a thing. We never thought that would ever happen now that he's not in AEW in Chicago at Survivor Series While WWE product just it's the hottest it's ever been in a long time.  No, they don't play that They don't play people sending tweets out about other wrestlers. That's not in a storyline situation like trying to they don't They don't do that.  So that's why I wouldn't have I wouldn't worry about The potential issues that he may have because at the end of the day We we may hear about it, but it's not gonna it's not gonna be something that's Overshadowing what's happening on the show because at the end of the day They'll probably keep that shit for the most part under wraps as much as possible But they're not gonna let no shenanigans go on for too long that WWE does not play that They will let somebody go quickly before they deal with some BS like that negative press in that way Like the company don't know how to manage the wrestlers. So comment down below. Let me know Are you guys wanting to see CM Punk return at this year's Survivor Series? Or are you guys cool with him staying wherever he is at right now? But I appreciate all of the support you guys show on channel well join VTK And I'm still getting speedy YouTube wrestling champion world. Appreciate y'all kicking it with me. See y'all next week. Peace


Welcome to module 45, Ticknoff's theorem. So, Ticknoff's theorem is a land mass result in the development of point set topology. The key result that we are going to use as a step for Ticknoff's theorem is that this is called Alexander's Sub-Based Theorem, an expiatorological space and fix a sub-base S for its topology. Then X is compact if and only if every cover of X by sub-family of S admits a finite sub-cover for X. We have seen that if X has a sub-base such that open covers from this sub-base, from this base they admit a finite sub-cover, then X is compact that much we have seen already. But Alexander's Sub-Based Theorem goes one step ahead. It says instead of base you can just use a sub-base. The proof of Alexander's Sub-Based Theorem itself is not very straightforward. So, we shall postpone the proof of this one, but use this one to prove Ticknoff's theorem. Okay, so once again I repeat that Alexander's Sub-Based Theorem essentially cuts down the verification of compactness of a space from arbitrary open covers to open covers coming from a single sub-base. So, that is the whole idea. Ticknoff's theorem can be stated as follows. Start with a family of topological spaces, each of them non-empty. Then the product space X i is compact if and only if each X little i is compact. Okay, what we have seen is that if the product space is compact, each factor space is compact. Of course, for this you have to use that that X i's are non-empty. Therefore, the projection maps are surjective. A surjective continuous function takes compact space to compact. That is very easy theorem that you have proved. Using that, you will follow that if product space is compact, then each X i is compact. Now, we have to prove the converse. Assume that each X i is compact. Let S be the standard sub-base for product topology which we have been using, namely consisting of all p i inverse of u i for all open sets u i inside X i and for all i inside i. By Alexander's sub-base theorem, if we show that an open cover from S, you know members of S, that admits a finite sub-cover. That is enough. Okay, any arbitrary open cover but members are from S, if that admits a finite sub-cover, then X will be compact. So, that is what we are shown now that starting with an arbitrary open cover with members of S, we will show that that is a finite sub-cover. So, for each i in i, put u i equal to dose u i inside X i such that this p i inverse of u i is in S prime. This S prime is the sub-cover that we have chosen, it is a cover that we have chosen. Members of S prime cover X. From this, we want to extract the finite sub-cover. So, first I define u i, this is a sub-family members of open subsets in X i.  Then each member of u i by the very definition is open in X i. Okay, we claim that for at least one i, u i is a cover for X i. Okay, we have not claimed that all the u i's will cover corresponding X i here. At least for one of the indices, this must happen is what belongs there. If not, what happens?  For every i, this will happen. Okay, so pick up one point X i in the complement of this.  Now, X is in some member of F say because this is my this S prime here. Okay, say X belongs to pi j inverse of u j for some pi j inverse u j belonging to some S prime that is what for some j. This means that if X belongs to this one means its jth projection is X little j, which we have chosen must be inside u j and with u j belonging to some curly u j. That will be our prediction because we have chosen this one to be such that they are in the complement of all this. Okay, so therefore one of the u i's will cover the whole of X i.   Okay, it follows that pi p 1 inverse of u 1 j's, you take p 1 inverse of these things will form a finite sub cover for X sub i from S prime. There are members of S prime that is how we have chosen. But this is now cover because X 1 is the union of all these things. So, p 1 inverse of all these things will be the whole inverse of cover for X i and these are members of this one. So, that completes the proof. Okay, that completes the proof of Tyknoff's theorem. There are several proofs of this important theorem. Indeed, it is a fashion with every aspiring topologist to give his own proof of Tyknoff's theorem. Never mind that only a few of them may succeed. Nevertheless, there are quite a few, quite a few proofs of this theorem. Okay, now let me give you an example here. Namely, our favorite example are with semi-interval topology, lower limit topology or sorry, general fry topology and so on. There are various. This we have seen earlier several times. This space is a Lindelow space. So, let G be a family of semi-open intervals which cover R. So, I am trying to prove how it is a Lindelow space. It is not very easy to see. It is enough to show that this admits a countable sub cover. So, I am using that this S is actually a base here, open subsets of the form a comma b, a closed and a b open. That is the definition of this topology L. Okay, take a cover by these open sets. There is no need to take unions of these things and so on. This is a base so we can take this one and then show that it is as a countable sub cover. Okay. So, what do we do? We will use the property of R in the usual topology and then compare it with this one. So, put u equal to union of open intervals a, b where this a comma b, a closed, these are members of this G. Okay. So, we started with G, a family of semi-open intervals which covers R. Now, you drop out the first point here in each interval. Okay. And take only open interval a, b. Then this union will be clear in open subset of the usual topology in R. But now the usual topology is second countable. Therefore, it follows that there exist a countables of family a and b and contain inside G such that this u is union of countable many open sets. So, what I am using is every open subset of a second countable space is second countable. Therefore, it is a Lindelof. Okay. If I just use directly R u is Lindelof, I do not know how to, this one is Lindelof because it is an open subset not a closed subset. Okay. But if you say second countable, then every subspace is second countable and second countable spaces are Lindelof. So, you get a countable sub cover for this subspace u which is an open subset. Therefore, why I have put y or u whatever it is, why u is open. Okay. Now, I put back all the a ands but only taking from this countable sub cover, put y equal to union of bracket a and n, put back these points. This may not be the whole of R. If that were R, you are fine. See, we dropped out all these starting points of the interval. The initial point of the intervals you dropped out. Now, you put back. But that may not be the whole of R. However, it is not difficult to see that whatever is left out, namely put f equal to R minus y, what are they? They are all the starting points of intervals a comma b coming from g. Some of them, some of them are already here in this countable family. Some of them are left out. That space f equal to R minus y is definitely a closed subspace. It is a discrete set. No open interval will be contained inside that one. The open parts have been taken care by this a and b n, open a and b n. So, that is easy to see that and hence it follows that f is countable. Once f is countable, you pick up open subsets which cover f for each one of them, one open subset from g. Along with that, you put all these a and b ns also, which you have got already. Together you get a countable family that will cover the whole of R. So, that shows that the semi open interval topology is Lindelof. But now I am going to show that the product is not Lindelof. See that was my idea. To show that we showed products, even infinite products and so on of compacts which is compact. And we are all the time telling that Lindelof property keeps tagging on. So, this is one phrase where it does not. Even product of two of them need not be Lindelof. So, take x equal to R s cross R s R l. I should be taken l because I have used this notation l here. So, look at that is not Lindelof. For if it were, then the anti diagonal x comma minus x, x belong to R. We have used this one earlier. The anti diagonal being a closed subspace will be also Lindelof because closed subspace of Lindelof space are Lindelof. On the other hand, given any point x comma minus x in delta hat, delta at Videl, consider the open subset you know first closed x comma x plus 1 or x plus R whatever cross minus x comma minus x plus 1, some positive number minus x plus not necessarily 1. You take these open subsets. These are open subsets in this x namely R l cross R l ok in the product pathology. Alright. What is the intersection of this one with the anti diagonal? It will be just the first point x comma minus x ok. So, intersection with the subspace delta at Videl is just the single term. That means all the single terms are open in delta at Videl in the subspace topology. It just means that delta at Videl is a discrete space. However, it is its cardinality is the cardinality of R. It is uncountable ok for each x inside R that is x comma minus x. So, an uncountable discrete space cannot be lindeloff ok. So, product is not lindeloff even product of two of them. So, this is the picture I have taken. This is the anti diagonal x comma minus x in R cross R. Open subsets of this product space are of this nature x comma minus x plus s ok. It is x comma minus x, x plus R comma minus x and then these the dot dot dot these parts are not there in the open path. But these two lines are there intersection of that one with the anti diagonal is just this point ok. So, that is a picture for showing that the anti diagonal is what is a discrete subspace. So, we have given an example of lindeloff. So, we have shown that product is compact if each coin is compact, but the lindeloff property is not even finite productive ok. Coming back to this Alexander sub base theorem let us get a little bit familiar with one of the central results in set theory which is very useful especially in topology and algebra. Of course, we are going to employ this immediately in the proof of Alexander sub base theorem ok. So, a little more point set topology here today and then we will wind up today. Tomorrow we will again proceed with Alexander sub base theorem. So, this is about partial orders and so on. So, start with a set which is partially order preferably non-empty ok do not take empty set and by a maximal element in x we mean x belong into x such that x is less than or equal to y for some y will imply x is equal to y. So, there is nothing sitting over x. So, that is the meaning of maximal element alright. Note that there may not be any maximal element inside x. Like if you take r with the usual order it has no maximal element that means it is not bounded right. So, there is no maximal element. Also there can be more than one maximal element ok. So, you can think about you know if you take some subsets of any set then put a inclusion map it is you can have bigger ones one bigger one bigger here those two are not comparable and so on there are lots of such examples alright. So, maximal elements may exist and also there may be plenty of them also either of them can. Now there is another simple definition by a chain in a partial order set we mean a subset of the form whenever x and y are inside this subset either x must be less than or equal to y or y must be less than or equal to x ok. Of course, both of them happen that is also allowed but then x will be equal to y that is by definition. In other words why is a chain if and only if under the restricted order it becomes a totally order set that is another name for it totally order set always has this property ok. A totally order subset of a partially order set will be called a chain. So, we have just introduced another word here which is popular in the in the point set you know point set theory that y be a subset of some partially order set. An element z inside x is called an upper bound for y if y belongs to y implies y is less than or equal to z. So, this is an upper bound. So, all these things are very you know very straightforward definitions. But these definitions are now made in arbitrary partially order set that is what you have to be careful not inside r or q or integers and so on. They will of course apply to r, q all those things also. So, this is a general partially order set alright. Now, here is what is called as John's lemma which is almost like one of the axioms of point set theory you know set theory as such equivalent to axioms of choice. John's lemma says that start with any non-empty partially ordered set. Suppose every chain in this x has an upper bound then x has at least one maximal element. It does not say anything about uniqueness of course there may be plenty of them. It just assures you there is a maximal element okay this is John's lemma alright. So, next time we shall use this one very effectively to prove Alexander's sub base theorem. Thank you.


Loan lights. Here's the statement. This is a statement from JFK Jr., right? Or RFK Jr., right? Backing dollar and U.S. debt obligations with hard assets could help restore strength back to the dollar, reining inflation and ushering the new era of American financial stability, peace and prosperity. My plan would be to start very very small. Perhaps 1% of issued T-bills would be back by hard currency, by gold, silver, platinum or bitcoin. Yeah, I can see that for sure. And that's what every individual should be doing, right? You want to diversify. So it's not all by bitcoin. You should have gold, silver, platinum, maybe haven't looked into platinum too much, and cryptos, possibly bitcoin, right? 100%. Okay, the kicker is most people don't appreciate that. One of the ways you can back to currency, fax simmer, 789. Thank you very much for subscribing. Salute, salute. Salute, salute. To your one sub, subscribe for 22 months. FX simmer, 785. Thank you very much for being here. But here's one thing that people need to understand. One way you could back the currency is increased interest rates, right? Especially during wartime.


our stewardship of creation for future generations. Although the UK and Scottish Governments have made progress in some areas, we need to do more. The Scottish Parliament has the power to make further progress, let it do so. The Scottish Conservatives will continue to push the Government to get on with the job that it is tasked with rather than focus on powers that it does not have. I would like, before closing, to commend my parliamentary colleague Stuart Stevenson for his humourful contribution to today's debate. I have benefited from his sense of humour since standing for the Scottish Parliament in 1999 at Hustings against Stuart. We were all very enlightened by his comments on what the Queen's grant of permission to enactment of a piece of legislature can do for domestic relationships. I thank him again for that contribution, Stuart. I also wish that Stuart and the Scottish Government well in recovering from what appears to now be a chronic state of self-induced brexitas. As my colleague John Scott said, you have a job to do. Get on with it. I call Mike Russell, 10 minutes, please, minister. Thank you very much, Deputy Presiding Officer. Can I start by declaring an interest? As others have done, I have been the species champion of the corn cake and the tree lungwort, but not at the same time, I want to stress. The purpose of these debates, Presiding Officer, is to try and discover common ground to hear new and positive ideas. That is the same idea that is motivating the meetings that I am having with party leaders and much of the discussion that I am taking in across Scotland. Unfortunately, what we have learned today and we learned at the very outset of this debate is that the Scottish Conservatives do not want to take part in that process. Mr Golden was actually very testy about it in his opening speech. Finlay Carson also poo-pooed it, although I am very glad to see that my reasonable friend John Scott welcomed the fact that those debates were taking place. The reason, Presiding Officer, that the Scottish Conservatives do not want to take part in those debates is that they expose the emptiness of their position. If the debates are about bringing ideas and imagination to help Scotland to move forward, they are found wanting. I think that bringing ideas and imagination to the chamber and standing up for our constituents and for Scotland is our day job. So, let me suggest to the Scottish Conservatives that they get back to their day job, they take up their day job and start bringing some ideas and thoughts to this chamber rather than simply complaints. I am delighted to be involved in this debate, not at this moment, Mr Scott, but I will let you in later on. I have some more to say about Mr Scott, which will be positive, of course. It is a pleasure, even with the little advice that I have left today to support my friend Roseanna Cunningham on environmental issues. She succeeded me as environment minister in February 2009. We agree, I think, that the job is the best job in government. I am delighted that it is now a full cabinet rank. She is a great defender and advocate of the Greener Scotland. Her skills, her passion and her knowledge will be needed as never before, because the environment must become a key issue in the Brexit negotiations. It is already clear to me, from the discussions that I have, that the UK Government is not really interested in this issue. It is low down their list of priorities. So, the Scottish Government can help the UK and Europe and might even say immodestly the planet by making sure that it takes centre stage. It has been a pleasure to hear in this debate Claudia Beamish and Mark Ruskell. The three of us are three of the five nominees for the nature of Scotland politician of the year award this year. The other two are Richard Lockhead and Sarah Boyack. I am putting the smart money on Sarah Boyack for her contributions to the chamber, and it is probably important to mention that here, because this is a debate that she would have relished and she would have contributed to with great distinction. But, to less happy matters, Mr Golden opened the debate by saying, I believe Brexit means Brexit. Later on, Mr Burnett told us that we are leaving the European Union and we are going to make a success of it. Just as there was a little red book of Mao quotes, there is now clearly a little blue book of Theresa May quotes, because those are direct quotes from Theresa May, but it will take more than quoting the little blue book to convince anybody in this chamber and anybody in Scotland about the reality of Brexit. What we are hearing from the territories, as the First Minister said this morning, is not collaboration or co-operation, it is capitulation. We are hearing nothing at all that stands up for Scotland, that puts the case for the Scottish case in Brexit, and that was a last true of what Mr Golden had to say. It was Mark Ruskell who made that point almost immediately, because he pointed out that the reliance and the Tory motion on the UN agreements will allow, would allow and undoubtedly will allow the UK to weaken environmental protection, just the type of agreement that the Tories seem to want. He pointed out, if you wanted proof of it, the damage that has been done by the Tories to the renewable infrastructure, since they decided to start reducing the subsidies. If we look for evidence of what the Tory position on Brexit will be on the environment that we see already, it is a desire to weaken standards. Unfortunately, I would have liked to have heard Liam McArthur supporting that, because it is the first time that he has taken part in one of those debates that he said, and he opened very strongly. He said that Brexit was not in the Scottish or Orkney communities interests. He said that EU membership was profoundly in the interests of this country and its constituents. However, the logic of that position would surely put him in the support of ensuring that all the options are considered for the future. Until the Scottish Liberal Democrats are prepared to consider all those options, they are not alas being true to that objective. Liam McArthur? I am very grateful to the minister for his generous remarks. As I pointed out in my comments earlier, yes, Orkney voted in favour of remaining part of the UK, but it voted overwhelmingly more so to remain a part of the UK. That, I would have to say, remains very much their interests. Michael Russell? Mr McArthur is not being asked to make that choice at this present moment, nor are his constituents. What Mr McArthur is being asked to do is to be part of considering the options for the future. Unfortunately, by refusing to consider all those options, he is not taking that forward rationally. Kate Forbes made a very important contribution on natural capital, and it is worth observing that Scotland is the first country to have a natural capital asset register. If I can refer to another contribution that followed immediately on to it from it, Mr Burnett, having talked about making a success of Brexit, then, unfortunately, he said something about the Scottish referendum in 2014 that must be corrected. He said that he understood that those who voted would have the knowledge that people would vote to leave the EU. Well, not everybody did, I have to say, because I refer you to this statement. No means we stay in. We are members of the European Union. That was from Ruth Davidson in September 2014. I give way to Mr Burnett. Just a correction for the record. However, when people voted in the Scottish referendum, they did so in the awareness that there was going to be another referendum, not what the result was going to be. I repeat the quote from his leader. No means we stay in. We are members of the European Union in September 2014. People, unfortunately, were misled by a number of people, including the leader of the Scottish Tories. I was delighted to know that Stuart Stevenson was the species champion for the Spiny Lobster, but I was also delighted to have his testimony, which this chamber has heard, that in terms of climate change, there was always a lack of support from the UK Government, something that should make us even more nervous going forward. Let me come now, Presiding Officer, to two last contributions. John Scott's a reason contribution. I disagree with it, but there was an alarming indication in it of what a future Tory tactic will be. John Scott was demanding that this Government addresses and funds every possible application under pillar 2. That seems to be a tactic that, having been criticised over many years for not replacing every cut from Westminster, we are now to be criticised if we cannot replace every funding shortfall from Europe. That would be unreasonable, and I hope that Mr Scott, who is not an unreasonable man, will reflect on it. Finally, let me address Gillian Martin's points on research and the wider issues of research. It is vitally important that we look at every issue in the Brexit debate, not simply as a self-contained issue in devolution, but as well as reflecting wider issues. The wider issues of freedom of movement and the wider issues of funding for research really depend on us being part of the EU and engaged with the EU. The problems that we will have in researching the environment will grow enormously unless we are engaged fully with Europe. Mr Lindhurst summed up in a calm manner, I think that I would describe it as that it is important that we do more, that we have more engagement. He did not explain how, and I got a little confused by his contribution. It appeared to me what he was saying, that we should give up the European Union birds directive that protects, for example, if I may mention it again, the corn-crake, but we should sign on to the CETA Convention that protects elephants. I do not think that those are mutually exclusive, but it does seem to be rather confusing to prefer corn-crakes to elephants and to use that as a reason for leaving the EU. Finally, I quote Gillian Martin, Presiding Officer. She said very memorably the most memorable line in this debate to the Tories. If you do not like hearing about grievances, stop causing them. That is the reality of the Brexit situation. The Tories have put us in this situation.  Come to the table with ideas and debate it sensibly. So far, we have not heard that.  That concludes our debate, and we move on to the next item of business, which is decision time. There are five questions to be put today. I wish to remind members that, if the amendment in the name of Maurice Golden is agreed, the amendment in the name of David Stewart, Mark Ruskell and Liam McArthur fall. The first question is that amendment 2125.1 in the name of Maurice Golden seeks to amend motion 2125 in the name of Roseanna Cunningham be agreed. Are we all agreed? We are not agreed. We shall move to a vote, and members may cast their votes now. The result of the vote on amendment 2125.1 in the name of Maurice Golden is as follows. Yes, 27. No, 87. There were no abstentions. The amendment is therefore not agreed. The next question is that amendment 2125.2 in the name of David Stewart be agreed. Are we all agreed? We are not agreed. We shall move to a vote, and members may cast their votes now. The result of the vote is as follows. Yes, 87. No, 27. There were no abstentions. The amendment to the name of David Stewart is therefore agreed. The next question is that amendment 2125.3 in the name of Mark Ruskell is agreed. Do we all agree? We are not agreed. We shall move to a vote, and members may cast their votes now. The result of the vote on amendment 2125.3 is as follows. Yes, 83. No, 31. There were no abstentions. The amendment in the name of Mark Ruskell is therefore agreed. The next question is that amendment 2125.4 in the name of Liam McArthur be agreed. Are we all agreed? We are not agreed. We shall move to a vote, and members may cast their votes now. The result of the vote on amendment 2125.4 in the name of Liam McArthur is as follows. Yes, 10. No, 104. There were no abstentions. The amendment is therefore not agreed. The final question is therefore that motion 2125 in the name of Roseanne Cunningham as amended on the environment and climate change European Union referendum be agreed. Are we all agreed? We are not agreed. We shall move to a vote. Members may cast their votes now. The result of the vote on the motion in the name of Roseanne Cunningham as amended is as follows. Yes, 82. No, 31. There were no abstentions. The motion as amended is therefore agreed. That concludes decision time. I close this meeting of Parliament.


Here awaits. Written and illustrated by Alyssa B. Chapter one, form spring day and I have finished celebrating my seventh birthday. I was walking my sweet pup, Mr. Jellybean, in the forest near my house, wearing something shining in the distance. We ran over to it and it was a strange looking metallic and it smitten with numbers on it. I pressed the numbers 2040 and a door appeared. I opened the door and we were in a place with flying cars and there were some houses floating in the sky. Where am I? Mr. Jellybean, I asked. Chapter two, a girl came up to me and asked, are you excited to go up to Mars? Mars, I said. There's some reflection on the window and I looked older. She said, aren't you Isabella Kingsley, the first astronaut to live on the moon? I was speechless. My childhood dream had come true. I need to find out if I was dreaming. So I pinched myself. Ouch! Miss Kingsley, are you okay? Can you tell me why you became an astronaut paleontologist? She asked. I took a deep breath and told her my story. As a child, I used to dig in my backyard, looking for fossils and spend the evenings looking at the moon with my telescope. I'm curious, adventurous, hardworking, creative, patient-persistent, funny, passionate, brave, and an explorer. Wow! I also saw in the newspaper, you discovered Spidosaurus. What was that like? She asked. I couldn't believe it. I had found a dinosaur that hasn't been discovered. I told her I feel like it's out of this world. Newscape, June 6, 2040. Isabella Kingsley discovers Spidosaurus, a new dinosaur discovery of Isabella Kingsley. A Spidosaurus has eight legs and looks like a stegosaurus with spider legs. Chapter three. So much fun living as an adult working in my future dream job by miss being a kid. I was in my apartment talking to my parents in a 3D screen when I noticed a strange metallic instrument in a plant. I pressed 2-0-2-2 and I was in bed in the forest with Mr. Jellybean. I can't wait for the future so I can be an astronaut and a paleontologist.


Can Josh Allen win a Super Bowl with the New York Jets? I plopped him straight onto the roster to find out. We end season one, eight and nine. No Super Bowl, but a promising future. Just kidding. We end season two at six and 11. We're spiraling. Season three went more or less the same. But then, season four. At mid-season, we're four and two. Josh is up to a 96. Breeze Hall's an 86. We got this guy. And the Jets make the playoffs. We went 13 and four, and after battling through the playoffs, the Jets made the Super Bowl. We face the New York Giants in Super Bowl 62. The sim begins. The Giants leap out to a lead and is...  Maybe next year? Five and 12. It's not happening.


What's up everybody, Jason here for Jasper's Case Breaks dot com. We have a little 1920 panini prison basketball retail one-pack break Number three filler which is gonna give away four spots in the Black Mamba mixer So again guys the way this works is first we will randomize the customer names and Teams distribute the hits out of the one-pack retail and then at the end of the break We'll randomize the customer names again in a separate dice roller randomizer and the top four names will win a spot in the mixer So let's do the break first really quick. Let's roll the dice and we got ourselves a three and a four for seven times Good luck one two three four five six seven Seven times Steve down to Zach seven times One two three four five six seven Dolls Mavericks down as a Brooklyn Mets All right again really quick Lance Rex you have the pelicans Grizzlies down here Anthony bro with their heat Kim with the Lakers There's the rest of the teams right there All right there you go Hey Rex, I've seen I pulled silvers out of these packs, so it's not gonna shock me If I were to pull in here or even a base is all we need So let's see. Let's see what we got here. Oh, we got an autograph. Wow Thomas Bryant. Wow We actually got an autograph on this Malik Monk and Lucanard fire Jake Elliott. All right guys just like that. I Dice roller here. Here's the customer names again Roll it remember top four get in after one and a five six times. Good luck One two Three Four five six Six times top four get in Anthony Roger Rex and Kim there you go six times Top four get in congratulations guys. There should be another one posted I think and if not, I'll post one up right now guys. Appreciate it. Jasper's case breaks.com


Alright, what's going on everybody a little promo for tonight's transcendent we did fill it up So appreciate everyone getting in we have about 33 people who bought spots straight up in this transcendent today So thanks everybody top five names win $100 in break credit I'll try to send those out tonight so you can use them on the website in the morning When the break is or when the website is filled up so four times one into three One remember top five win $100 each two three fourth and final time good luck for There you go Here are the names who won CJ Alexander B.J. Dustin and BJ Congrats so BJ you'll get $200 Dustin $100 Alexander $100 and CJ $100 So appreciate it. Thanks everybody for getting in really appreciate you guys and gals filling up this transcendent tonight So thanks everybody peace


A new program. A great program. The Moore Durante Show is coming to CBS. Tune in every Friday at 10 p.m. Eastern wartime beginning tomorrow night for laughs with Jimmy Durante and Gary Moore, and music with Georgia Gibbs and Roy Parkes Orchestra over most of these same stations. This is the man in black here again to introduce Columbia's program Suspense. With us again as star is Mr. Orson Welles in the third of four successive appearances for the Suspense audience. And sharing honors with Mr. Welles this evening is a lovely and distinguished Hollywood leading lady, Miss Geraldine Fitzgerald. Our play tonight is from a short story by Agatha Christie. And so with Vila Melkotic and with the performances of Geraldine Fitzgerald as Alex Martin and of Orson Welles as her devoted husband Gerald. We again hope to keep you in suspense. Vila Melkotic. What's that, Alex? I was just reading the sign over the gate. What does Vila Mel mean? Are you joking? No, really.  You've been here for three weeks and you still don't know. Vila Mel is another name for the birds. It's supposed to sing only for lovers. You've been hearing it every twilight. Oh, Nightingale. Of course. That sign, Vila Melkotic, is the main reason I wanted this place for us. Glad you bought it. Harold, this is a 50-50 investment and you know it. 50-50, a thousand pounds from me and two from you. What else could we do? You couldn't touch any more of your capital at the time and... Well, when you find a country cottage that combines old world charm with new world plumbing, we want to grab it. And we did have to have this place, didn't we? Yes, we did. I was wondering if you went a bit lonely. Lonely? With you? I mean, well, after living the city all your life, pretty much to ourselves, you know. Two miles from the nearest neighbor. The nearest eavesdropper, you mean. Not an utterly hopeless romantic, I mean. Well, you can't get out of it now. Oh, Gerald, you know what day today is? Today? It's the 13th. It's our anniversary, darling. We've known each other exactly a month. No, exactly 30 days. Oh, Gerald, really now. Oh, really? What is it, dear? Do you have the painting? No, there's no indigestion, I think. There? Do you want me to get you a pillow? No, no, no. Well, yes. It's 11.25. It'll get on to the village. Now to get that camera equipment. And the human time table walks through the garden gate. My dear, there's nothing wrong with system, even on a honeymoon. Sooner I go, sooner I get back. Oh, come on, Gerald. Forget the old photography. Why don't you stand do some gardening to be good for you? Better for old George. He gets paid for it. He's not due again till Saturday. The place will go to Rackenwood. Oh, my dear buddy. Bye, dear. Don't walk too fast, dear. Remember the last time. Be careful, darling. It had just slipped out. Be careful. Alex Martin swinging there on the garden gate. Smiling out a happiness across a part of England that was as remote and placid as any you care to find.  If this were London, say, that would have... London. Slowly the smile fell away. She knew then that the memory of that last week in London had never really been far from her mind. That and that last talk with Dick from the top deck of the bus crossing Trafalgar Square. She'd never seen him like that before. Gerald Martin.  You know nothing about him. How can you know in a week? You've only met him. It doesn't take everyone seven years to find out you're in love with a girl. It's meant for me, isn't it? Alex. It's no use. Alex, don't you know what it's been for me not being able to tell you? I couldn't, not with the anger myself. Then I decided I couldn't wait any more and I was going to tell you anyway. And you know what happened? No, I'm afraid I don't. Oh, yes, you do. That money you inherit. That money from your cousin or uncle or whoever. That money? I'm sorry, Dick. Believe me, I am, but it really doesn't matter now one way or the other. Doesn't matter, does it? You can bet it matters to that Martin chef. That's what he's after. You mark my words, he's after your money. Dick, it's my interest you to know that Gerald has money of his own far more than I have. And more than I have. Maybe that's the difference. I've had enough of this. I'm getting over the next talk. Alex, please. All right, but let me tell you something. If you think I'm going to let Gerald cut me out of what they do here, I'll catch up with him if it's the last thing I do. I'll catch up with him if it's the last thing I do. To Alex, that threat of just one month ago was merely a season-to-moment outburst of her pride. And yet, as she leaned on the gate of Philamel Cottage, it kept echoing in her mind. What swept it away? What brought her back to the rustic, idyllic happiness of a life with Gerald Martin? It was the ring of the telephone inside the cottage. Who could be caught? Gerald is hardly had time to get beyond the turn in the road. Except if something had happened to him, he'd had another attack. Maybe one of the villagers was trying to call to say that he... but she hurried down and her hand shook a twig. Hello? Who did you say? Dick? Being you're here? No, no, you mustn't. I'm sorry, Dick. I... I only meant to be away this afternoon. Won't you come this evening? Goodbye, Dick, and I hope that... she stood quite still, the memory of Dick's threat flooding her mind. She walked across the spacious, old-beamed living room. By the time she reached the side porch, she'd made up her mind. Much as she hated the seat, she would say nothing to Gerald and Dick's call. She stepped out into the garden and for the second time that morning got a surprise. There, Bigger's life was her garden, fizzily trimming her head. Hi, George. I thought it would be a surprise, Mrs. Martin. There will be a fair over the squares on Saturday. I said to myself, I said, Mr. and Mrs. Martin, they won't take it a miss if I come this way once on a Wednesday instead of a Saturday. No, of course not, George. Then I thought, too, as I might as well see if all you do is away, so as to earn your wishes with the borders. Before I go away... To London, tomorrow. Hmm, going to London, tomorrow. Where did you hear that? Mr. Martin down the village yesterday. He's only was both going away to London, tomorrow. And it was uncertain when you'd be back again. Oh, I didn't. Now don't tell me you and the masters this is waiting already. Hmm? Oh, no, naturally not. The tip just slipped my mind. Get on with your work, George. Yes. Never could understand why anybody wanted to go up to London, no. Like historians, like you used to have this house. You went up there. Now, shall I remind you? Yes. And after fixing up this place like he did, tax all over everywhere, well, you're going to take a loss, I says, to him when I seize the place up for sale. I think everyone is well, you're a fan for washing yourselves when we're speaking. But George, he says to me, he'll get every penny of 2,000 pounds for this house. And sure enough, he did. He got 3,000. 2,000. Some he was asking was taught job at the time. Very hard to figure it was thought to be. No, George, you see, I gave to London. Well, it really was 3,000.  He didn't say it to me, he said it to me. I guess I'll do some speeding now. The price was 2,000. As Alex strolled on across the garden, she was conscious of a thin, thick fork struggling to make itself heard. Then abruptly it was gone. Her eye had fallen upon a small, dark green object lying in the fur beside one of the flower beds. Her husband's pocket died. She picked it up and opened it. Scamming the entry was some amusement, once again reminded of Gerald's enslavement to time and system. It was the entry on page 21 that brought the smile from her face. April 14th. Smell, Alex, St. Peter's Church, 2,000. And it was the entry on page 30 that took that smile away. She stared puzzled at the date on the page, when she made the tea. Why, why that's today? Only one thing was written there in red pencil. 6 p.m. 6 p.m. As she stood there, that small, big thought struggled to be heard once more. It was... Yes, it was something big-winter that it said. Not the threat, not that wild, silly promise of vengeance, but something else. And then it changed. You know nothing about him. Nothing about him. It was true. But did she know about him? After all, he... Gerald, my husband. I love him. I trust him. Then she thought once again of that cryptic entry. P.M. Just three o'clock when Gerald, his arms laden with packages, walked up the garden path and came onto the side porch. Well, Alex... The moment he opened the door into the living room, he noticed the rather odd kind of excitement about him. There you are. Miss me, darling. Why wouldn't I? You've had time to buy out the whole village. Only the camera, sir. Now, I don't have the best equipped dark room this side of London. It won't be my fault. If you're not careful, that dark room of yours is going to overflow the whole cellar. Oh, incidentally, here's something you've been watering the flowers with. Cat. Diary. Dropped it in the garden, didn't it? I know all your secrets now. Not guilty. I'm not so sure. What about your resignation at 6 p.m. today? Well, that's... Well, you've caught me at last. It's an resignation with a very handsome young woman, quite remarkably like you would say. You're evading the issue. Not at all. Simply a reminder that I want you to help me develop some negatives this evening. At six o'clock. That's rather peculiar time, isn't it? Peculiar? Yes, I'm usually preparing dinner at that hour. No. No harm in delaying it a bit. We might have a sandwich or two and some coffee out on the porch. Before we walk on the negatives, you mean? Yes, that'll be pleasant, won't it? You know something, Alex? I've never found anybody yet who could touch your coffee. Oh, really? That covers Australia and Canada, don't you? You and your mysterious past. Why do you say that? No reason, I... Oh, Gerald. I do wish I didn't know more about you. I know, it's silly, but I... Darling. I've told you all about me, my boyhood in Sydney, my life in Canada. Yes. I see. You mean love affairs.  Well, but there must be another woman. There must be another woman. I mean, if only I... Do you think it's wise, Alex, this blue-beared chamber of business? Let's put your mind on such a subject anyway. Have I mentioned it before? Oh, I don't know, Gerald. I've been on it upset all day. I imagine I can thank old George for that. Oh, my God, do you mean? He had some ridiculous idea. We were going away to London. Where did you see him? He came to work today instead of Saturday. Me, oh, fool! Gerald! I didn't get this. Oh, Gerald, lie down. Here's some water. Here, darling. I'm all right. Oh, I'm sorry, darling, getting you all upset.  I made some weak joke to him about being off to London in the morning enough to take it serious, as it didn't help. It was straight in the mouth, I suppose. Hardly.  I didn't want the whole village to think my husband was eating me in the dark about his plans. Are you all right, ma'am? You... you told him we were going then. Naturally. Sorry you were placed in that kind of situation, darling. I don't suppose you... ran into anybody else today. Is this often the word, Gerald? It isn't very likely, is it? Gerald. No, not another word. No, not another word. You aren't yourself, and that's quite plain. I want you to have a little rest. You'll be right as rain by six o'clock. Must you do that set of graphs tonight? After all, you don't think so well, you... My dear, if one one sets a time to do something, one should stick to it. The only way to get through one's work. All right, up with you, upstairs to bed now. Very well, dear. I'll be getting things arranged in the dark room. Well, Alex, rest was more like a nightmare. Upstairs in her room, she told herself that there was no basis, no basis whatever for her state of mind. Still, the turmoil, the doubt, the unaccountable sense of dread persisted and grew. Grew until... stepped out of the upstairs hallway. Quite clearly, she knew what she must do. She knew she must find some testimony to her husband's past, something to reassure her, something to kill that agonizing dread mounting within her. Strangely, she remembered that single locked drawer in Gerald's bureau. She dipped over the door ahead of the stairs, opened it, and entered her husband's room. Yes, the key. If only she could find the key that locked the drawer. But there was none in sight. She moved to the wardrobe, went through his coat pockets, and then there at her feet, there on the floor, she saw it. Swiftly, she stepped to the bureau, inserted the key, and it worked. Alex Martin opened the drawer, looked down upon a small packet of letters tied with a light blue ribbon. And when she saw the uppermost envelope, her face reddened with shame. Why, then? Why, then, my letters? They were her own letters, love letters written to Gerald before they were married. And there was nothing else in the drawer, save a roll of ancient faded newspaper clippings. Alex sighed with relief as she glanced at the top clipping. It was from an American paper, and it featured the trial of one Charles Lamentra. Oh, Lamentra. A notorious swindler and bigamist. A skeleton had been found beneath the floor of his house, and most of the women he'd married had never been heard of again. Another of the clippings described Lamentra's behavior in court. His interest in the cameras of the news photographers, his sensational escape from prison. Another displayed his picture, a long bearded scholarly-looking fellow. He reminded her of someone. But who? She couldn't tell. She glanced at the caption beneath the picture. Modern blue beard. Modern blue beard. That's what she read. Her eyes went back to the picture, and in a flash they saw the resemblance. She ran through the other clippings. Dates had been found in the man's pocket diary. Dates was contended when he had done away with his victims. He was an amateur photographer. He was from Sydney, from Canada. He was subject to heart attacks. He was. He was. He could try to warn her. They could be near her that morning. She turned him away. She turned toward the brightened pipe in the corner, running up through the room. From below, near its base, something was striking that pipe. As though someone were digging, the matron was comparing the dark room for the latest one of his victims. Less than an hour from now. Suddenly, all the jigsaw pieces shot into place. The money paid for the house. Her money. Her money only. The bond she didn't trust her for his keeping. Suddenly, she heard no sound. The digging had stopped. She must have escaped from this house at once before he came up to clip him right back in the door. Don't lock it. Don't allow it. Just get away. She rushed to the door, out to the hall, out to the door. She startled me. I was just trying to find her nail file. Well, that's nothing to look so guilty about now, is it? Come on down. Getting late, you know. Just have time to make the coffee and sandwiches before we do the pictures, that is. I'd be right down, darling. Oh, but we really mustn't delay, must we? Coming, Alex? Yeah, let me give you a hand. There you are. Cold. Yes, I am. Well, that will soon pass away, I'm sure. Hurry along, dear. Hurry along? Alex, what is the matter? Nothing. I'll be all right. The kitchen. Yes, I'll fix you something in a second. You just sit here in the living room and... No, the porch. That'll be more comfortable, won't it? And I'll be right with you. Well, of course not. What, dear? How rotten of me not to have suggested it. Since you're feeling a bit under par, you can probably do with some help. I'll come with you. That someway, somehow, she must get word to Dick Winterfell. The fact that he might be gone by now, the memory of him telling her so, she resolutely put out of her mind. There must be no more panic. She must be in utter control of herself. Alex carrying the coffee out of the porch, glanced at the clock from the mantel, ten minutes till six, her very life hung by those next ten minutes, by her ability to think coolly and swiftly the cost tending beside her was a man as determined as he was insane. Pity you're so abstracted, my dear. Pity you're so abstracted, my dear. What? Why do you say that? Well, because you are missing the loveliest sight you'll ever like to see again. Why do you say that? We are in the garden. First soft shades of twilight. Mm-hmm. Twilight. Over thrill of male cottage. Now, I say, Alex, you are below par. What do you mean? First time you've ever slipped on the coffee, must have topped in the entire canister. I'll be more careful, Oculus. Oh, dear. Alex, where are you going? What is it about, Gerald? I forgot to order meat for tomorrow. I'm just going to find the butcher. The butcher this kind of evening? He generally stays late on Wednesday. I'll be right back, darling.  It keeps the insects out of the living room. You're not afraid I'm going to make love to the butcher, are you? Operator, get me the travels arms, please. Hurry. Travels arms. Mr. Winterford, please. What? Well, see, won't you? It's most important. Don't let me disturb you. Well, darling, you do.  But I do, Gerald, truly. You're quite sure you're really calling the butcher? Well, as a matter of fact, I'm not sure. What? What I mean is... What are you talking about? I'm afraid I've got the wrong person. A perfect stranger. You don't understand. Someone I know nothing about. You know nothing about, then why don't you hang out? Here was the fan of that wireless. Hello. All right, my girl. I'll go get started. We're late now. Besides the three minutes past six. Why, Gerald, it won't be six o'clock for eight minutes. Look at the clock there on the mantel. I don't go by that, Relic. I go by my own wrist watch. Well, listen, stop pacing and listening to me. Well... I don't feel up to it tonight. I'm tired.  I'm not going to wait one minute longer. I won't do it. Come along, Alex. I'm not crying with you. No! You will, you will. I've got something to tell you. Something to confess. Yes, to confess. Something I was too close to before. I've had... I've had my secret past, too. For my love, I suppose. In a way, but... But something else. You'd call it, yes? I expect you'd call it a crime. Yes. I don't believe it. Yes. You better... You better sit down, Gerald. There. I... I told you I'd never been married before. That wasn't entirely true. There was a marriage. When I was 22, he was an elderly man with a little property. I induced him to ensure his life in my favor. At one time, I was a nurse with... with access to a number of poisons. There's one poison, a white powder. It... You know something about poisons, perhaps? No, I know very little about them. This one is very much like... it's absolutely untraceable. Any doctor would give a certificate of heart failure and that... and that... I can't... Another time, Gerald. Another time now. I want to hear. How did you get him to take it? How did I get him to take it out? Yes. Well, he always made his coffee for you. Coffee? Yes. One night I put a pinch of this... of this poison in his cup. I remember that evening how very much like this it was. How peaceful. He gasped a little. I had to move from his chair. Presently, he died. How much... How much was the insurance money? About 2,000 pounds. I speculated. I lost it. It was over two years before I... before I married again. He was a much younger man, quite well off. There was a will in my favor. He liked me to make his coffee, too. Just as my first husband had done. I make very good coffee. It was the same, along about twilight. I remember it perfectly. I'm nervous and upset I'd been all day, but it turned out all right. But it did. It was the same as the other. He just sat there in his chair and... and he died. My husband did have a weak heart, you see, and that... that helped a great deal. That netted me over 4,000 pounds. I didn't speculate. That's why I tasted that, where you tell you poison me. Poison me! Yes, poison is working. You see? It's all moved from your chair. I'm lying.  You can't move, you're helpless. There's nothing happening in that room. You can't. It's the trouble to call me up and talk about someone you knew nothing about. Excuse me, sir. The man sitting in his chair. It looks like so. Yes, we'll see. He did. Your husband named... You might say a perfect stranger. That's sitting in his chair. And... in presence he... he died. And so closes Philomel Cottage. Agatha Christie's story of love from a stranger starring Geraldine Fitzgerald and Orson Welles. Tonight's tale of... suspense. This is your narrator, the man in black, who conveys to you Columbia's invitation to spend his half hour in suspense with us on October 19th, when Orson Welles will again be our star. Our next broadcast in the series will be Tuesday, October 19th at 10 o'clock eastern wartime, 7 o'clock pacific wartime. The producer of suspense is William Spear, who tonight also directed the broadcast and who with Wilber Hatch, and Lucian Malowick, conductor and composer Harold Medford, the radio author, collaborated on tonight's... suspense. It's CBS. The Columbia Broadcasting System.