Proudly, we hail. New York City, where the American stage begins, here is another program with a cast of outstanding players. Public service time has been made available by this station to bring you this story, as proudly we hail the United States Army. The warlords of ancient Japan with their samurai swords would have known the central character in today's story, a dim figure from the past tenuously attached to life, to being, to sanity. This is the man we meet in today's program, the Gaunt Man. We'll let the mystery unfold for you in a moment, but first, young men, when you volunteer for service in the United States Army today, you can rest assured that your best talents and natural skills will be considered in giving you an assignment to your liking. Yes, today's modern army fits the right men to the right jobs, and real merit is recognized with faster promotions and more opportunities. Now, more than ever before, men with above-average ability are finding better jobs and more important assignments in the United States Army. Why not investigate an Army enlistment for yourself right now and find out just what you stand to gain? Full information is available at your local United States Army recruiting station. And now, your United States Army presents the proudly we hail production, the Gaunt Man. Tokyo, Japan, that's where I work. I'm in headquarters company of Central Command of the United States Army Forces Far East. The fellows call me Gil Hui, but my name's Gal Hui. Master Sergeant Tim Gal Hui. Well, sir, being in Tokyo is great. I like being here. I have a flock of real intelligence soldiers working with me. Real intelligent. Radio specialists, announcers, script writers, linguists, translators. Almost everything. So when something happens, I'm not too surprised. Yesterday, I was working over a report, and this happened. Here's the mail. And what a load. Strength figures show a slight increase in personnel. You all right, uh, toss me the company mail, huh? Yeah, I think there's one here for you. Mm-hmm. Yeah. Here. Great jumpin' Texas horn toads. Dowry. Private Dowry, front and center. Oh, look, Sergeant, I cleaned around my area twice this morning. Read this. Holy smokes. Yeah, holy smokes. How'd this happen? Well, it's a long story. Do I have to tell you? Well, as a matter of fact, you don't. Just, uh, just tell the captain. But being as I have certain jobs to be done once in a while... Yeah, yeah. Let's see. It started at the, uh, Takatazuka Ballet. The what? The Takatazuka Ballet. You know, the Japanese follies. Oh, I get it. Keisha girls singin', dancein'. Yeah, that's right. Well, I bought two tickets. One for Corporal Matthews. Anyway, we got there pretty early, and that's when it all started. Good seats, huh? Yeah, except that my knees touched the rails almost. I never knew I was so tall until I hit Japan. They're still good seats. The first row balcony. Hey, incidentally, this is gonna be great from what I hear. Colors and the kimonos will be out of this world. Now, I've got an idea. If we could get some real close shots, they'd be collector's items. So we got half an hour. Let's ask the manager if he'll let us take a few flash pictures backstage. They don't want the American army backstage. Two men, not the whole army. I bet very few people have asked to do it. They're even thought of it. Come on. Let's go. You are the first Americans to want to come back here. Please make yourself at home. Well, thank you. If I may say so, these are very clever gadgets for changing scenery. Yes, we have been doing it for a long time. When you were still chasing Indians, we were changing scenery. That's right, at that. Oh, my friend here says that he saw an American working back here. Oh, yes. We have a foreigner working for us. He is an excellent craftsman. Understands what we want. Well, isn't that a bit strange, sir? I mean, an American designing Japanese scenery? Indeed, it is. And this man is very strange. We call him Arodo. It means the gunt man. Well, that certainly fits. The skinniest man I've ever seen outside of a circus. I wonder if we could talk to him, sir? Certainly. You go over to the third door. You see? Yes, I see. Arodo is in there doing some painting. Well, thanks a lot, sir. Thank you. Why do you want to see him, Joe? This is a natural. Right in the middle of a Japanese extravaganza, we find an American who understands their art. They call him the gunt man, the boot. Let's write out an Edgar Allen poem. Yeah. Third door, he said. Yeah. There's two. Look, this guy is probably an ex-soldier who married a Japanese girl and settled down here. That's all, maybe. This is three. Let's go in. We're just looking around, sir. The tree has been down to thank the water. I think he's nutty. Let's get back to our seats. Yes, yes, they do. They look really artistic. You're an artist by profession? Artist? If this is art, I am an artist. Well, I mean, were you trained as an artist? When the sun comes up, these trees lift their heads to the sky. He's screwing it. That's true. Did you go to art school in the United States? Look, if you please, this must be finished. I must show that trees are grateful to the eternal streams flowing from Fujisan. Oh, thank you, sir. I'll come see you again. Perhaps I can show you how I paint a mountain that is worshiping Buddha. Thanks very much for letting us walk. Yeah, yeah, thanks. All the nutty characters. Oh, right. That fella's in trouble. Trouble? He just slightly touched, that's all. He thinks he's a Japanese Rembrandt. Something's wrong. And I'm going to find out what it is. Hello, soldier. More pictures? No, sir, no pictures this time. I want to ask you a few questions about the gauntman. Yes, I knew you would. You did? Yes. You are curious. You sent something? I think there's a story somewhere, maybe even a tragedy. Soldier, you are an intelligent man. Just imagine it if I think. There is a story. A prominent Japanese businessman asked me to hire this man. Do you think that there's a mystery behind this man? If I were an American and I met a man who acted like the gaunt, one, yes, I think I would go to this address. What, ten? Ichikom-kyoto? K-kyoto? I will go there. Forget where you got that address, please. My friend is too prominent to offend.  I understand, sir, and many thanks. I went to Kyoto with Corporal Frank Matthews. Frank didn't want any part of tracing the gauntman, but he did want to see Kyoto, the fabulous city of a thousand shrines and hundreds of temples. We were lucky, places near the station. Nice house. It's an old one, look at the carving. Shall I knock again, do you think? No, I think I heard something. May I help you? Wow, what beauty. We're looking for Mr. Gomi. He is my father. He is away now. I am very sorry. Could I help you? Perhaps you can. If you'll excuse the remark, you certainly speak good English. At Kyoto University, English is a must. I have had four years and two before that in what you call high school. I see. Well, I was going to ask your father about an American that they call the gauntman. He works backstage at... Is something wrong? I am quite all right. Please, won't you come in? Well, if we're not interrupting. Oh, no. Over here, please. Um, Midori Suzuki. And I'm Private Joe Doherty and this is Corporal Frank Matthews. I am glad to know you both. Thank you. This is certainly a lovely home. The little garden just inside the front entrance. Is that a Kyoto custom? In old houses, yes. This house is very old. We will have tea in just a moment. Aroto, is he well? Well, I don't know exactly how to answer that. We only saw him a few times.  Yes, I know. Could you tell me something about him, Miss Midori? I... I think the gaunt one will always be rather strange, foggy, cloudy. I have the feeling that there's a story connected with him. I feel that maybe I can help him some way. No, no one can help him. But if you'd tell us about his background, we could try. You do not understand, Private Doherty. He lived with us for a while. Everything has been tried. But father had to send him away. He said that I had too much pity for Aroto. He said... And this is very true, that pity is too close to... to love. Could you tell me how the gaunt man got here in the first place? It is very vivid in my mind. Near the end of the unfortunate war, we were driving from Tokyo to Kyoto. Kyoto was not being bombed, you see? We have always been grateful for that. Of course. Anyway, we were on the open road and we could see the shell bursts of the anti-aircraft shells and the airplanes coming over, going north to Tokyo. Suddenly, we saw an airplane get hit.  It fell to earth, not far ahead of us on the road. We drove on, talking about it. And I think I was the first to see the man climbing out of a ditch. His face was badly bruised and his clothes were ripped and he staggered as he walked. He still had a parachute dragging behind him. We picked him up and brought him here to Kyoto and found that he could not be moved. And that was the gauntman? Yes. That was the gauntman. You are listening to the proudly-we-hail production The Gauntman. We'll return in just a moment for the second act. Ever stop to think about the meaning of a military salute? Soldiers call it a sign of recognition between men of an honorable profession. Some historians say the military salute began when knights in armor raised their helmet visors with the right hands to show friendliness. In our time, it's come to mean among soldiers a gesture of respect, not just for the individual himself, but for the uniform he wears and the nation it represents. That's worth remembering. Next time you see a soldier in the uniform of the United States Army, keep in mind what his uniform means. It's a visible symbol that he wears proudly if he's a good soldier. He's a master one of the most honorable professions in men's history, a sign that he's joined the good company of generations of American soldiers who have done man-sized jobs in the defense of our beliefs. He's a man to respect, and he deserves your salute. More, if you can qualify, he deserves your help because our country needs more men to stand beside him. Visit your United States Army recruiting station first chance you get and find out how you can help him if he's doing well. You're listening to Proudly We Hail. Now we present the second act of The Gauntman. So, Dorothy, the way I get it so far, the Japanese Army didn't raise a fuss with Midori and her father? Well, I think he was a high-ranking officer. Well, don't keep me on tent pegs. Go on. Let's see. Corporal Matthews and I sat there listening to Midori's story of how they had tried to discover who The Gauntman was. I wonder what would happen if our Gauntman saw somebody who knew him in the days before he fell out of the sky. Hey. I beg your pardon. Hey, what? I'm beginning to get an idea. Camp Otsu must have a signal court film library. If it does, and if the place where you, Midori, picked up The Gauntman is near here, we have a chance. Maybe only 50-50, but we have a chance. The place is not very far, but I do not understand. We're going over to Camp Otsu and fast. We've got to talk to the noncom who runs the film library where they store army films. Maybe to the soldier who checks out the projectors. Who wants to see a movie now? It's not what you think. I think we have a chance to clear up the mystery of The Gauntman. Do you really think you could? Midori, I'm going to give it a good try. Just so long as we don't run over all leave time.  Not if we work fast. Midori, could you get in touch with your father quickly? I'm sure I can. He's near Tokyo? Yes. Well, tell your father that two American soldiers think they can establish the identity of The Gauntman if he'll bring him back here to Kyoto. Yes. I know he won't want to do it. Well, maybe you have some influence. Make it strong about the chance we have of finding out who he is. Will your father try it, do you think? I think that if my father realizes that it means much to me and I think he does already, and that there is a chance he will bring him back. Good. Frank and I'll go to Camp Otsu. And Midori, please, start trying to contact your father right now. Please, be seated. We can talk freely. Harudo is sleeping. He has been working very hard. He loves his work.  Yes, sir, we do. If you'll excuse the rush, we must work fast. I'm on leave. And we've got to use the films at the time arranged for us. Films? Yes, sir. They fit in with the idea. And then we might need a car, a taxi would do. I have a car. Good. Sir, do you think that we could disturb Harudo? Time is going short. I think it will be all right. One thing, we must not make his condition any worse. That I will not permit. Father, is not anything worth a try. He cannot get much worse. He might just possibly get better. These are his countrymen. I think we should help. Yes, I suppose so. Fine, sir. Let's go to Camp Otsu as soon as we can. They call this the screening room. It's a small theater, as you see. The army holds classes here, and the men are shown various army films. Oh, Frank, how many different reels did the sergeant give you? Three. One from the Korean War and two old ones from World War II. All taken in an airplane? That's what the tag says. Midori-san, do you think he's ready for this? I do not know exactly what you are going to do. Whatever it is, I want you to try it if there is even just a little possibility it will help him. He has not changed in years. Look at his eyes. I know. I've always thought of them as haunted. Yes, they are haunted. He is haunted by fringe memories that he cannot grasp. The first film is ready. Let it roll. I looked from one to the other in half darkness. They were all leaning forward, tense. Even Corporal Matthews. This was silent film, but it was powerful. It had been taken inside an airplane during the war in Korea. We could see the tenseness in the faces of the gunners and sometimes we could see glimpses of the rough terrain below in the towering mountains. And then the film was over. Lights went on, we all turned and looked. It had had no effect on the gaunt man at all. After all, that no effect at all? What about this letter? You're getting me confused. Well, there's some more. I stopped because that was a disappointing thing. 20 minutes of aerial combat and no effect. Well, what happened then? Mr. Gomi got restless and wanted to leave. Then good old Matt saved the day for me. He'd gone back to where the projectionist was working the movie machine. Midori was uncertain herself. Now we were with a bomber crew over Germany in World War II. Again the men were sober and intent and again Midori watched the gaunt man's profile closely. The airplane began to toss and swirl.  The airplane held straight, flew right through the burst, and then it rocked violently as bursts came closer. Oh! Oh, it was too much for him. Break the light. He has fainted. I was afraid of this. Haroldo, can you hear me? Yes. Midori said my head hurts. I was really in the soup. Not yet. Not quite. Look at his face. It is like paper. It has not helped at all. Well, it was just a gamble, Midori son. It was just a gamble. Look, how about the other part? You said something about needing a car. Oh, no, I don't know now. What was supposed to get to the spot where he came down, right? Yeah, that's what I planned. Well, let's go then. Mr. Gomi, let's get over to the road you were on the day he came down. This was the road that you came down to when you jumped from the blazing airplane. All right.  This man and this girl. Please, he looks torture. Let him try. This is the last pitch. Joe thinks he's close to something. Maybe close to remembering. You were in a bomber. It was flying low. You flew through and an aircraft fire. Just like you saw in that movie. It was all around you, but you flew through it just like the airplane in the movie. And then you were hit. The airplane burst into flames. This is too much. Please, Midori-san. He must finish it. He's trying to remember. Look at his face. Yes, daughter. Something is happening. His face shows it. You'll perish to die. You were the only one who managed to do it. Floated down just about here. You hit hard. Very hard. He doesn't remember. I was afraid of this. Joe, you're not going to give up now. He's trying to remember. Look, why not have him walk along the road and have Midori and her father pick him up? We've tried everything else. Midori, would you mind trying just one more thing? What? If you will, drive back a bit and then stop and pick him up. Frank and I'll get out of sight and we'll start him along the road. I never thought Mr. Gomi would go along with this last-minute attempt, but he looked at Midori's face and he climbed into his car without a word.  We waited a minute and then started the gaunt man walking down the road. It wasn't hard to do. He was dazed and I felt sorry for him, but I had to finish what I started. The car came up the road as we walked towards it. Frank and I then stayed behind and the car stopped. I saw them talking. The gaunt man climbed in slowly. Too slowly, I thought. And then they drove on towards us. Well, Frank, that's that. Well, let's see what happens first. I can tell you're ready. He's probably asleep. Midori is crying. Wait a minute, wait a minute. This suspense is killing me. Get to the ending. Well, after Midori called out to us, Frank and I ran over to the car. The gaunt man was sitting there quietly enough. He was pale, but, well, he was always pale. Midori was smiling, sort of a wobbly smile, but it was a smile and her father had his arm around the gaunt man's shoulder. Well, I didn't waste any time. I started right... He is remembering. Let me talk to him. Sir, do you remember anything at all? I don't know. I think so. Oh, do you remember when the anti-aircraft guns began firing at you? Do you remember being in an airplane? Yes. I was in an airplane. And the ACAC hit you, didn't it? Yes. There was anti-aircraft fire all around. And there was an explosion. And then you found an exit. A side door was blown off. And you jumped? No, no. The airplane began to fall. And I fell out. Well, when you hit, you hit hard. Yes, very hard. I saw a tremendous flash of light. The wind blew me so that I hit the ground with my head and shoulders, and I was dragged. Oh, his memory is flooding back. This girl and this man. Now do you remember them? Don't overdo it, Joe. He's shaking. I'm getting close to it now. This girl and this man, they were driving in a car like this on this very road, just about here. Yes. I remember it. It all comes back. It seems so very long ago. It was so long ago. I wanted, and I witnessed story of a bombing raid, but I couldn't get permission. They didn't want correspondence on the airplane because there were too many being shut down. I managed to slip onto one ship that I knew was going on a raid. And they found me after it was too late to turn back. The pilots. I remember clearly now. He was a nice fellow. He insisted I wear a parachute. He said he was going in low. You do not need to continue now if it is hard for you. No. No, I must talk. It's sweeping back to me. I remember that I had forgotten my identification cards. All I had was a notebook and a fountain pen. It's getting clearer now. I'm sure of it all. It all connects. Why couldn't I remember before? Well, sir, I guess it took the shock of living part of it again. Whatever the cause. I'm grateful, soldier. This is great. Now the important question. Who are you? Yes. Who are you? I'm Francis Connolly of Montreal, Canada. I represent it. I guess I should say that I did represent a chain of newspapers at last. Oh, this is wonderful. Soldiers, you have done a very wonderful thing. As we watched this man's rebirth, we knew why the American Army and its investigators couldn't find out who this man was. He was a Canadian. No one knew he had even been aboard the plane, not even his own correspondent friends. Well, Private Dowdy, I asked for the story and I got the story. I must say it was a good one, too. That explains the letter all right. I couldn't imagine why the Canadian government wanted you to report to the liaison officer of the Canadian Army attached to this headquarters. Now, the captain's late. You'd better get back to the barracks and get into a fresh uniform. There'll be a lot of pictures taken when they pin on that medal. Young men, today's United States Army is made up of skilled technicians and specialists who have learned their jobs in the world's finest military technical schools. And now, the Army is offering you even greater opportunities to join this elite group of young men and serve your country and yourself at the same time. If you're a high school graduate of service age, you visit your nearest United States Army recruiting station and make application for the Reserved for You training program, stating your preferences of branch and training course. If you qualify and a vacancy exists, you're awarded a letter that guarantees you a reserved seat in the technical training course of your choice.   We suggest you find out about it right away by visiting your nearest United States Army recruiting station and talking it over with the friendly people there. This has been another program on Proudly We Hail presented transcribed in cooperation with this station. Proudly We Hail is produced by the Recruiting Publicity Center for the United States Army. This is Ralph Rowland inviting you to tune in this same station next week for another interesting story on Proudly We Hail.


What is going on guys welcome back to the channel critical overload here So let me talk about screen 5 as this is the week that we should be not necessarily getting overly Excited about it But a small smidgen of an exciting expectations for us to have something Described at least about screen 5 coming out of Cinemacon this upcoming Thursday This is the week of Cinemacon Paramount will be having its slate of films coming up presented for a time slot That I think runs a little over two hours, maybe three And we're all of course a screen fans anyway We're anticipating that we'll get our first Official look at screen 5. It won't be released to the public But it'll be released and shown to those in attendance at the Cinemacon Paramount panel Now I just want to kind of use it chapter 2 and Halloween 2018 as a reference on what we could potentially have Coming our way this upcoming Thursday So this upcoming Thursday what could end up happening is that they actually do talk about screen 5 Maybe there's even an official synopsis brought out or maybe even an official poster But the other thing that could happen, of course, we know is they could show footage They could show footage made whether that be a one-long sequence of things from the film or just a short teaser and This would be very similar to what it chapter 2 and Halloween 2018 did back in 2018 at Cinemacon They had shown the trailer and there were little descriptions that were coming out on social media after the trailer came out Of course, it wasn't released to the public till a couple weeks later Same thing happened for it chapter 2 with that whole Beverly scene with the old lady from it chapter 2 Descriptions came out because it was shown at Cinemacon and everyone was just waiting to see What this actually would look like when the footage got released online So it's not that it's not that Unreasonable to expect that would be the same thing that happens with screen 5. I believe That there is of course a 50-50 chance of them showing something and then not showing something if they do show something It's not going to be released to the public What will happen though is that you'll have those in attendance who are allowed to give out very Descriptive descriptions that aren't maybe depending on what they saw and what they want to and not have disclosed They could still give descriptions and that'll just build up the hype for this footage that they all saw that will now be Anticipating the scene we could get again Like I said an official plot synopsis that goes into more detail as to what screen 5 will be about not just a young woman Returns her hometown to investigate a series of vicious crimes which doesn't point the finger on who said young woman is whether that be Sam Carpenter Tara Carpenter, Sydney Prescott or even another woman that we don't even know about yet. So we could get that But if it's the footage the footage whatever it may be whether that be a short teaser a one-minute long teaser Or maybe a minute and a half teaser or just a a scene that is from the film Where we should expect what will happen is while it won't be footage that we see released It'll be the same thing that happened with it chapter 2 in Halloween 2018 You'll get some descriptions that start appearing online for those who were in attendance at Cinemacon and then weeks later Presumably during Halloween kills. That's when we will see the teaser or whatever it is trailer for screen 5 Because honestly What they could also do because it hasn't been officially announced to be one of the things that they show at the fathom event After Cinemacon this Thursday and as the release for the 25th anniversary screen is nearing They could officially confirm They hey if you know if you go out to this fathom event that we're having in the month of October this upcoming Sunday and Monday October 10th and 11th. You'll be one of the first First few individuals who will be getting their first look at screen 5 because we already have expectations that scream a bloody A bloody legacy 25 years later the feature it with all the new cast a mixture of the old cast and the directors Will be shown during that we know other vintage interviews will be shown during that I'm not sure how early you'll have to arrive there to start seeing that stuff I'm positive you'll probably have to get there by at least Six o'clock at best six o'clock at best if you want to see that stuff, but The other thing just going back to the footage the footage itself whether that be released online or not I don't think it will be the thing we should expect is just something very descriptive What could that footage be this again could be maybe Scenes that are just spread out across the film And like a compilation, you know, like they do with trailers a typical trailer and we just get people talking about how they saw Sydney what Sydney looked like what did what did gale weathers look like what did Dewey Riley look like What did ghost face look like because they could even start showing ghost face in this footage But of course it won't be released to us and we get another description of what ghost face was doing in the trailer Maybe ghost face kills someone or maybe maybe we'll even get to see something in the trailer once it's actually released to everyone Maybe there's something that gets shown at cinemacon that shows ghost face using something other than the traditional buck knife And we'll get descriptions of that. They start appearing online Thursday after the Paramount panel at cinemacon There's a plethora of things that could be shown. I hope that it's at least a poster an official synopsis And then right along with that some type of footage the footage is I think a must I think that's a must they don't they don't have to of course do it But I feel like when we're so so close to the release it might not feel close to a lot of you feels very close to me We're not that far out from the release date at this point It doesn't do you any harm to show the footage at cinemacon Show something at cinemacon and then have the full fledged teaser or trailer Whatever you want to do release during the release of halloween kills and then piggybacking off of the attention That halloween kills is already expected to get When it comes out on october 15th In that would just be another cool type of nod to the times that halloween and screameth have referenced each other Scream 2 being shown on screen in halloween h2o Randy and his and his friends and stew watching the original halloween in the original scream and talking about that movie And talking about jamie lee curtis and etc etc I just think that would be another cool thing as we think about the the references that have happened between the two franchises To have the trailer come out during the release week of halloween kills uh But I know a lot of you have already purchased your tickets for the fathom event that's taking place in month of october So who knows what will happen on thursday? I just wanted to say that I think what we should expect is that if footage is shown Expect descriptions of said footage to then be released online. Don't expect it to be shared with us Hopefully this footage does of course have sydney prescott so we can get some descriptions about What sydney prescott is doing maybe we'll even see certain things Maybe certain things are shown that indicate what her next career move has been since she wrote that book Maybe they'll show certain things that indicate what gail weathers is up to and dually of course Uh, maybe we'll get confirmation about that divorce that we all are assuming to be true between the two And we'll hopefully get to see things between the new cast members and learn more about sam carpenter Hopefully from the descriptions that again, I expect we'll start coming out on thursday after the footage is shown at Cinema con if it happens But let me know what you guys think about this down in the comment section below if you haven't already make sure you subscribe Turn on post notifications at never miss a video in the description. I have links to my social media accounts I'll facebook twitter and instagram you can message me there Of course there's any movies deserve usually have me to cover in the future with all that in mind guys I will see you in the next video


Thanks, Bob. Well, we know it is not official yet. Erin, I have to ask you, what type of relief were you feeling today knowing that 99 is likely returning to the Bronx? Yeah, I mean, yesterday was a was a long that hit in my stomach all day. Uncertainty, rumors, tweets.  While you had that pit in your stomach, you also elected to reach out to Aaron and have a phone conversation. What was that chat like? Yeah, I mean, I'll keep that between us. But basically me just want to touch base with him and make sure he knows how I and we feel about him and just make sure and to see where he was. You know, I mean, he's obviously someone that's really important to to our team and our franchise, but someone that, you know, is important to me. And I just felt like I needed to at least, you know, as we get down to the finish line here, make it known and get a feel exactly from my standpoint where where I thought he was and make sure I communicated with him properly. Did you feel better after that phone call? Were you able to rest a little easier? I don't know about that. You know, maybe a little bit better. It was good to talk to him and to see where he was and see what was going on. And just just really, you know, really grateful to, you know, to how and what the Steinbrenner family just over and over just kind of delivers on these kind of things and and hopefully they were able to finish something off. Aaron, you talked last year about judge so often that sometimes you said you've ran out of superlatives to describe him. How would you describe a team that has Aaron judge back and as opposed to the the option of not having him back? I mean, it would be enormous.  And then just someone that, you know, I think leads our group and guys look to and look up to, you know, to have a superstar player that's also one of your culture drivers and how you want guys to, you know, if they model themselves after that we're in good place. So when you have a great player, that's also the best person too. It's a pretty dynamic combination. What was the response like from some of the other guys on the team? I would assume that you heard from some other players with excitement that he was going to make? Yeah, I mean, yeah, a couple of texts, obviously. And, you know, a couple of texts leading up the other way when we weren't sure what was going on and we were a little fearful. So, you know, I look forward to connecting with a lot of guys on the team here over the next few days and, you know, hopefully we get to a point where we're in a celebratory situation because we're bringing them back. We know as the Yankee manager what it would mean to you to have Aaron Judge in the lineup, but the baseball fan in you, the fact that Judge would be a forever Yankee and the fact that he would be a Jeter, a Pasada, a Bernie Williams, a guy who could play an entire career with the Yankees. What does the baseball fan in you think about that potential?  You know, I think he looks perfect in that uniform, but to have as, you know, as big a figure, a chance to be in a historically great Yankee, you know, those are the thoughts that kept me thinking, of course he's going to end up with us because he, you know, belongs on this team and, you know, on a Hall of Fame track and into Monument Park and into the Hall of Fame with that NY, you know, those are the things that you kept hanging on to and knowing how much he loves this organization, this team, his teammates, the city, all those things kept making me a little bit more optimistic even in some down moments. When Hal goes out and goes nine, three, sixty reported, what type of message does that send not only to the team, but to the baseball world? Yeah, I mean, you know, I think sometimes we take it for granted because over and over again, you know, Hal and the family deliver for us and it's something that, you know, we're lucky to be in an organization that consistently makes those kind of commitments and is involved like that and this case is right at the top of that list. You talked before about how he's a culture driver and sort of when the best player on your team is also one of the hardest working players. What is your favorite Aaron Judge anecdote from 2022? What is your favorite moment when as you reflect on the great season he had, there will be one moment that kind of embodies it for you? I think we were in Seattle and his first at bat, he struck out, didn't have a great at bat, came back and I even said something to him a little bit about the bat and he said, it's my bad, I got you. And he hits a homer's next at bat and as he's running from third base to home plate and we're in the third base dugout, he's looking at me the whole time like and he came back when he's coming through the dugout, he said, I told you. So he was apologetic for his lackluster first at bat and then answered with a dinger the next one. Well, one thing we know last season he did not have a lot of lackluster at bats. What will you remember from the home run chase? Um, man, I think the way his teammates over and over again responded. You know, I think they were genuinely more excited maybe than Aaron on through all of it in the days when it could have been potentially distraction like it never was because you I think it was a great indicator of just how much he's beloved because everyone felt such a significant part of it and rooted for it so hard. And to see the reaction from the entire team when he did get 62, I think gave you a little peek into just how special a person this guy is. We talk so much about his offense, but you've reiterated a lot of times how complete a player he is. When you watch him play the outfield, there are so many things to like, but the one thing I wanted to ask you about specifically are the accuracy of his throws. He's got this force seam over the top row and he's perfect almost every time. Yeah, he's just fundamentally such a sound outfielder and I think that goes back to, you know, the repetitions and the work that he's put in since he's been a very young player in this game in the minor leagues coming up. And what always strikes me about his throwing obviously has a great arm and he's accurate, but there's times when I'm like, I feel like I think he needs to hurry up a little bit. And he plays fast by taking his time though. So he never rushes himself too much, but always seems to just put himself in a great position to make a play. Have you spoken to him since the news broke? I texted with him this morning, but I've not spoken to him. What do you think that conversation will eventually be like? Um, normal, normal, you know, we've been at it together now a long time. So I think the conversation, if we're able to, you know, get to the finish line will be in, you know, where we go here over the next two months to get to get ready for what we hope is a championship season. Now, when I spoke to you earlier, you seem to indicate when we spoke to Brian Cashman, he seemed to indicate the work was far from done this off season. Do you expect more chips to fall here and you guys to acquire some more players? Yeah, we'll see.   Um, you know, the work never stops and trying to improve and, you know, hopefully we're still able to do some significant things the rest of the way this winter. You've talked about how you like your rotation. Brian has said the same thing, but as Meredith said, Brian has talked about the potential for upgrades. Carlos Radone is someone who is out there, great swing and miss stuff, tough guy, a talented guy, a guy who seems like he could be built for New York. When you see him, think about him. Do you envision a future where maybe he joins the? I don't know. We'll see. I mean, that's you're talking about a really talented guy that is obviously really starting to realize his potential in this game the last couple of years. So, you know, again, I think I think they're up there exploring every option and we'll see we'll see where everything ends up. How dialed in will you be now that you know this one chip has kind of fallen? Are you still as actively in the meetings in the conversations? Oh, no question. Yeah, I want to, you know, see where we're going, seeing what what possibilities exist, what combinations potentially exist. And, uh, yeah, hopefully we can continue to get a little bit better. I asked you earlier in the meetings about tinkering around with lineup cards and you said, well, the roster isn't set yet and it's still not set. We got a big piece though, right, right. When you put your head on the pillow tonight, might you just wonder where where number 99 fits in? Yeah, somewhere up up in that top of the order one, two or three, but excited to have our MVP potentially back in that lineup. What will the rest of the offseason be like for you? Going going back home tomorrow and, you know, kind of get ready for holidays and Christmas and have a family vacation coming up right after the Christmas. But we'll be in and out of the ballpark and and again just trying to prepare and get ready for for spring training and and, you know, so we hit the ground running. Well, nothing like a six eight present under the Yankees Christmas tree. How about it? Yeah, I love it. Erin, thanks for the time. Safe travels back. Bob will send it back to you.


Now that we've gathered the whales and brought them to a central point, we have to condition the gas before it can be put into a transmission pipeline. We do this in processing plants where we're going to remove a lot of the contaminants in our gases and extract as much of the heavier hydrocarbons as we can to sell them as propane, ethane, butane, etc. Basic operation of a processing plant for natural gas is to remove the heavy hydrocarbons. This protects the burner tip from volatile fuels such as propane and butane. They have a very high B2 content. Also by removing the heavy hydrocarbons, we manage to produce the much needed natural gas liquids, ethane, propane, butane, isobutane, and natural gas allines. There are various processes to extract the heavy hydrocarbons. The majority of natural gas liquids are produced through a condensation process. If you recall from high school physics, when you increase the pressure of something, you also raise its temperature. Then when you lower the pressure, the temperature cools down and condensation will occur. Another process is to use oils that can actually absorb some of the light hydrocarbons as the natural gas stream is passed over it. And finally there is fractionation where the natural gas liquids are moved from a composite stream into the various fractions, the propane, ethane, butane, etc. Another one of the operations of processing plant is to purify the gas stream. Raw natural gas coming out of the well has contaminants as well as inert gases which merely take up space. So the key here is to remove as much of the water as possible, the hydrogen sulfide, carbon dioxide, and nitrogen. Hydrogen can be removed using nitrogen rejection units at the processing plants. Dehydration can occur by using glycol absorption. Glycol is nothing more than ethylene glycol, the antifreeze that you would have in your car. Its boiling point is much higher than that of water. So when you boil the ethylene glycol, the water evaporates off of that. There is also a process known as amine treatment where sulfur can be extracted as well as carbon dioxide. There are various types of processing plants. The basic operation would be a simple separator tower. This is where the natural gas would flow through the bottom of the tower. The tower internally has collector trays and as the gas flows through the bottom to the top the natural gas or methane will rise to the top and move on out of the vessel and each of the liquids will lay on the trays based on their weight with the heavier liquids on the bottom. Using pressures and temperatures with compressors that will recirculate the natural gas throughout the processing plant and also reboilers, these are actually furnaces, the fuel by natural gas that will heat up the gas stream and then cool it down, hoping to knock out as much of the hydrocarbons as possible to create the natural gas liquids. Another form of plant is what we refer to as cryogenic. Most people think of cryogenic plants as freezing. The term being used here means to drop the temperature of the natural gas dramatically. You heat it up and then drop it as cool as you can. There are refrigerants used at the plant. You cool it down, you can expand the stream and then you'll cool down again and create condensation which knocks the liquids out and you circulate the gas for processing plant as many times as possible until you have approximately 98% methane which is then returned to the transmission pipe. The natural gas liquids are collected and brought to market. Another type of plant is known as a straddle plant. This is one that merely straddles the transmission pipeline itself, extracts natural gas from the pipeline, processes it and then redelivers the gas to the processing plant itself. It does not have natural gas wells gathered behind it. Here's a diagram of the generalized natural gas processing schematic. The first stage as you can see from the well head is to separate out any heavy oils from the gas. Then you have a condensate separator. This is where the water and some of the heavier liquids get taken out at first. The next phase is to totally dehydrate the gas stream, remove as much water as possible and then removing the contaminants. The hydrogen sulfide, carbon dioxide, nitrogen, et cetera. And of course then you can also remove the nitrogen using a nitrogen rejection unit or NRU. And then the demethanizer, again methane is natural gas. The demethanizer is going to extract the natural gas and return it to the pipeline on the residue side of the plant itself. And then finally the composite natural gas liquid stream is broken down into its individual fractions of ethane, propane, butane, the isomer of butane, isobutane, the pentanes which are also known as C5 pluses and then natural gasoline. This is data from the U.S. Energy Information Agency. This shows the increase in production in both natural gas processing liquids as well as liquefied petroleum gases over the years. There has been an increase especially in the last few years because of the new shale plays where there is oil. There is what is known as associated natural gas. It's produced in association with the oil. And as such it's very rich in hydrocarbon liquids and so it's processed. There are also natural gas wells that they themselves are high in hydrocarbon content so those get processed as well. The worldwide market for plastics has led to an increase in the demand for ethane. Ethane is converted into ethylene which is then converted into polyethylene and other plastics. Propane, pentanes, isobutanes have all seen an increase in the last decade. Here's just a couple of pictures of some processing plants in the upper left. You have a simple plant, small volume. You can see the tall tower there. That would be your separator tower. In the lower right you have a skid mounted plant which would be one section of a much larger plant. You would see multiple of these in a large plant facility but both of these plants are performing essentially the same function and that's to achieve condensation of airing temperatures and pressures and knock out natural gas liquids. In this diagram we look at the gas that comes into the plant and we're really focusing here on the amount of gas that is consumed by the plant or is knocked out in the form of natural gas liquids. So the heating content, the BTU content of the gas is reduced across the plant. We actually refer to that as PVR or plant volume reduction. You can see the diagram at the inlet gas is about a thousand MCF at a BTU content of 1.025 which is also known as the BTU factor. So we have 1.025 MMBTUs entering the plant and then you move over to the residue gas and you can see it's been knocked down to 967 MMBTU. The difference between those represents some of the fuel that is used by the processing plant itself but largely is the reduction in the amount of heating content that has occurred by knocking out the heavy hydrocarbons in the form of natural gas liquids. We're now going to talk about the individual natural gas liquids and the primary markets for them. This is again information for the Energy Information Agency which is part of the U.S. Department of Energy. You can see here that conventional crude oil and least condensate has increased over the last few years and is expected to continue to increase through the year 2035. This will no doubt be in large part due to the shale plays and the discovery of more and more oil in those shale plays. Natural gas plant liquids also are on the uptake and again mostly driven by the associated natural gas and the heavy hydrocarbon gas that's been found in some of the new shale plays as well as the increased demand for natural gas liquids in the global markets. The smaller amounts, you can see your unconventional oils, some biofuels and then again what is known as gas to liquids processing from natural gas. These are the main natural gas liquids components. These are the hydrocarbon liquids that are derived from natural gas. First you have ethane whose molecular symbol is C2H6, propane C3H8, butane C4H10, isobutane, the symbol for it is IC4 because it's an isomer of butane, the C4s. The pentane C5H12 otherwise known as C5 pluses and you have the natural gas saline, some are C5, some are anywhere from C6 to C9 and then condensates will all be, these are the heavy liquids, these will all be C6 pluses and generally speaking they can be moved to crude oil refineries and broken down into further products there. So each symbol represents the number of carbon atoms and the number of attached hydrogen atoms, thus the term hydrocarbons. As we mentioned earlier the NGLs must be removed from the gas stream, the BTU content will be too volatile for any type of burner tip use. They are used as chemical feedstocks, they're also used as gasoline blending components. The raw stream coming out of the processing plants for the most part is a composite stream known as Y grade. So these NGLs are basically ready for shipment by pipeline or by truck to other pipeline outlets, ultimately they head to a fractionator. Not every processing plant has a fractionation tower. The fractionation process separates the Y grade into its various individual component products, these are known as purity products, they represent approximately 90% of the single liquid for instance propane, ethane, butane. Let's start with propane, propane represents approximately 40% of the natural gas liquids market in the United States, primarily it's used for home heating and cooking. It also can be used as a chemical feedstock to make propylene for plastics. Primary markets for propane, Gulf Coast petrochemicals, Montbelview is the key natural gas liquid hub in the United States. It has a fractionation tower, it's a delivery and trading point. There are pipelines that deliver natural gas liquids to the plant as well as take away to markets. It has salt dump storage for natural gas liquids in the area and it is a global market in terms of the ability to export liquids to other countries from there. There's a secondary market in the Mid-Connard part of the United States located in Conway, Kansas. They have a smaller fractionation facilities there. Natural gas liquids Y grade are delivered to Conway. They also have storage on site. It is a trading point and there's petrochemical refining facilities adjacent to the Conway processing plant. There are pipelines that deliver natural gas liquids to and from the plant and there is southbound pipeline capacity to Montbelview for NGLs that cannot be fractionated at Conway. Ethane represents approximately 25% of the natural gas liquids market. It is a chemical feedstock primarily it is converted or cracked into ethylene and propylene for plastics rarely used as a fuel source. It can also be left in the gas stream as methane what we call ethane rejection. They are not recovering ethane they leave it in the natural gas stream. It is very price dependent. One has to equate the BTU equivalent of ethane versus natural gas to determine whether you recover the ethane or you leave the ethane in the gas stream. Same market hubs as other natural gas liquids Montbelview, Texas, Conway, Kansas. The term EP mix is used quite often when natural gas liquids are shipped in the form of 80% of ethane and 20% of propane and again that EP mix is strictly used for ethylene production. Utane or end butane as in normal butane 85% of butane is used for gasoline blending. It is mostly used in the winter when the reed vapor pressure of gasoline is high. Reed vapor pressure is as the footnote says indicator of the ability of the gasoline to vaporize at atmospheric pressure. So from the standpoint of emissions we do not want gasoline to have a high vapor pressure therefore a lot of it escapes to the atmosphere. Primary markets for butane, Gulf Coast and Northeast refineries. Market hub again Montbelview, Texas. It can be a cracking component for crude refining if you recall. In the presentation on crude there is one of the processes where some of the product is cracked. Some type of catalyst is used to crack it down to further products. Butane is one of those catalysts. One of the most obvious uses is as lighter fluid. It's also propellant and aerosol sprays. It replaced what used to be the CFCs or chlorofluorohydrocarbons which were deemed to have an adverse impact on the ozone layer. And so those have been banned and butane is one of the propellants that has substituted for the CFCs. It can be used household cooking also as bottled gas and it can be used as a refrigerant. Isobutane the isomer of butane, ibutane or sometimes known as methyl propane. It has similar uses to butane. It's used for gasoline blending as a chemical feedstock. It is also used as a refrigerant, especially in automobiles. It's known as R600A. And it's also known as iso-octane. It is an additive for gasoline that prevents the knocking when the octane level may be too low for particular engines. The natural gasolines or pentanes, these are the chemical symbols C5 plus. It's primarily used for gasoline blending again to maintain, stabilize the re-vapor pressure. Mostly in the summertime, the pentanes are added to gasoline. They can be used for ethylene production. They're also used as industrial solvents. They can be used for what is known as an ethanol denatrant. If you think about the production of ethanol, it comes from corn and grains. It is actually pure alcohol, the type of alcohol that could be consumed. And so something needs to be added to it so that people are, in essence, discouraged from drinking the ethanol. So the natural gasolines can be added to the ethanol as a denatrant, so it will not be consumed by humans, but it will be safe to burn in automobiles and trucks. It can also be used to dilute crude. And its major market hub is Montbelview, Texas.


Okay, in last lab we work with the pooling, but we learn how to work with the USART. Then now we can a little bit extend our knowledge with the USART and we add the new feature, we add the interrupt. Then now we can learn how to send and receive data with the USART together with the interrupt. For this we no longer need to use the terminal, but okay, if you want you can still use the terminal, but we create the loop back that we connect two pins together, then the data which we are sending we will also receive. This allows us to check if this also work and we can try in the same time the sending and receiving of data. Then for this I will start new project. I will start here new project. Again, I have the F4 family in my case, I have the F401 and my device is LQFP64 PIN package and it's STM32 F401 RET, 512 kilobyte of flash. Okay, my device is here, nothing surprising, then I can start here to pick up the USART. I can search for the 3 USART, but I know that the USART 2 is in my case on the NUCLO kit connected to the virtual comport, then I don't want to use this one, then I will try UART 1 and I can check in the user manual from the NUCLO if the UART PIN on the PA9 and PA10 are free. Then I will open my user manual, okay, I think in the user manual is also very nice table, maybe not, maybe not, then we need to check on our own. Okay, we will search here ESPA10 and unfortunately PA9 is not so close, that is really not so convenient for us, fortunately PA9 is completely different, yeah, here is PA9. Then for the intake connection I will use maybe very short cable, which I have with two connectors, it will be the best option. Okay, then I will search for my cable. Okay, I have my cable, then I can connect the PA9 and PA10 together to create my loopback, that it's the third pin from the bottom on the left, on the right hander, handler on the left side and PA9 is one, two, three, four, five, six, seven, eight, nine pins from the from the button, this one and it seems that the connection is okay, then now I can use the PA9 and PA10. Okay, this configuration is done, no problems. In the clocks I'm okay with the 16 MHz, always okay, and here in the configuration I first check the parameters, I'm okay with the bolt rate 115 200, because I have connected the transmitter and receive, then this speed is valid for the transmitting and receiving and I am also okay with all these parameters, also with the oversampling and definitely I want also the receive and transmit in the same time. If I look on the GPOs, I am also happy with the GPO configuration, also with the speed, also with the pull-up, I not see here any problem, but here I definitely, because I want to use the interrupt, I need here to enable the global interrupt. You can enable it here in the UART or here also in the NVIC, there is also UART and you can compare with the other pension priorities if you need to change the UART priority or not. Okay, and this is for the configuration part, now I can store my project, I will store it into my Atollic project, it will be called UART2 and it will be for the do studio, why not, I will click on the okay and I will generate my code, now we are asking to open my project.


Last time we had started the study of product of CW complexes. We interact, we begin a little bit but today we will continue our study. So what we have done was just to study one single example of S1 cross I. S1 with a CW structure with one zero cell and one one cell and the interval with two zero cells and one one cell. Okay, so the product we have decomposed when we want to think of some structure on a given space all that you have to do is as I have told you earlier decompose the space into open cells. Of course in a systematic way start with zero cells one cells if possible two cells and so on. You have to start with zero cells no problem. So you take S1 cross I the cylinder and then look out for the structure of CW complex which is some way related to the CW complex of S1 and the CW complex structure on the interval I. Okay, so look at the two zero cells zero cell and one cell in S1 denote them by sigma naught and sigma 1. Similarly I could have denoted the cells by cells inside I by tau and tau and so on but instead of that I will use the natural notation zero and one as one zero simplex and the interval I as the one simplex. With that notation in the product structure S1 cross I we have sigma naught comma zero sigma naught comma one these two will be the zero simplex. Sigma naught is the zero simplex here and zero and one of zero simplex is in I. So these two will be zero simplex it's been the product of space of the zero skeleton of the two spaces. What should be the one skeleton? The one skeleton should be zero skeleton cross one one skeleton cross zero all possibilities. So that way what we get is the one cell and zero cell and one cell is therefore different whatever different possibilities we have to take. So sigma one cross zero sigma one cross one these two are the one cells because sigma one is a one cell in S1 and sigma zero cross I I is the one cell on the other side ok. So that is the kind of thing what we have done. This is there are two zero cells here sorry one zero cell and one one cell two zero cells here and one one cell here. So we start with two zero cells sigma naught cross zero sigma naught cross one ok. Then this itself will become a one cell this will be another one cell and that will be another one cell corresponding to sigma naught sigma one cross zero sigma one cross one and then other one is sigma one sigma naught cross I. So the remaining cell whatever must be one single cell which corresponds to what sigma one cross I that will be the two cell right. So the theme is that this example completely tells you the entire story no matter what X and Y are most general case. All that you have to do is X cross Y decompose it into zero cells one cells two cells and so on K cells where K cells of the product will come from pick up I and J such that I plus J equal to K take all possible I cells in the one and the J cells in the other one take their cartesian product. So those things will be K cells for the product ok all the write down all the open cells that will fill up because X itself is a disjoint union of its open cells Y is a disjoint union of open cells the product will be each member here will take each member here to take the product. So that is theoretically completely obvious thing what we have we have a slight problem here because we have modeled our cells on the round model disk. The disk is the unit disk set of all unit vector sorry vectors less than or equal to norm one inside Rn. So that is a round model but we are only interested in things up to homeomorphism anything which is homeomorphic to a disk will be called a cell. Therefore we are free to choose any model and here when you pass to product a disk cross disk does not look like a round figure right it is not. Therefore you have a problem there so you have to change the homeomorphism type anyway you have to fix up dn cross dm to dn plus m a homeomorphism ok. So that has to be done whether you do that every time or you choose a different model is left to you. So here is a way of handling it right in the beginning we can fix up a homeomorphism from interval no problem but as soon as dimension 2 you come square and the round disk ok cube and the round disk and so on. So what you do take j equal to minus 1 plus 1 the interval let us have this notation standard notation like I have put i for 0 1 take j for minus 1 plus 1 take j power m that will be homeomorphic to the disk dm but now beauty is j power m plus n will be j power m cross j power n very canonically ok you do not have to fix up another homeomorphism here this is just a way of writing first k m coordinates and then last n coordinates right this coordinate wise the same maps are the same maps so you can say this is identification with this model the product structure can be easily understood ok. So fix funds for all just to go to our old definition our old definition used the model dn remember attaching cells was done from disjoint union of the copies of dn when you say copies that is already this freedom that you can choose whichever model you want these copies of homeomorphism ok so that is what we are going to do here fix up hn from jn to dn whatever homeomorphism you have some natural homeomorphism so the characteristics maps of attaching maps and the attaching maps are respectively from jn and the boundary of jn ok naturally boundary of jn also will not look like a round sphere now but it is homeomorphic sphere ok and one more thing set theoretically you should know that boundary of jm plus n is boundary of jm cross jn union jm cross boundary of jn ok these are set theoretically totally obvious so let us make a definition here in the most general case given two CW complexes X and Y we define the product CW complex X cross I have put a W there Y so this is to denote the weak topology little what we are taking X cross Y it is only SS set but the topology will be the topology that you want namely weak topology so how we are going to do this underlying set is the product set for each cell sigma in X and a cell tau in Y with characteristic maps phi and psi respectively we take product cell sigma cross tau in X cross Y which is characteristic map the product of the characteristic maps in particular observe that the zero skeleton is nothing but the zero skeleton of X cross zero skeletons Y with the discrete topology as usual start with that the one cells as I have told you will be zero cells cross one cells as well as one cells cross zero cells all possibilities you have taken that is the definition after that what you do inductively the case skeleton will be what X cross Y is space obtained by attaching to K minus one all sigma cross tau where sigma and tau range over cells of X and Y respectively the condition is the dimension of sigma plus dimension of tau should add up to K so that will be the case skeleton finally we give the weak topology on the union of all these case skeletons what is the weak topology something is clothed if it is clothed if it is clothed if it is clothed if it is intersection with the case skeleton is closed in the case skeleton inductively the attaching maps we do not need any new topology new definition because if Y is known and attaching maps are known then X is known so each case skeleton gives its topology already inductively but on the union I have to define it as the weak topology so this completes definition of what is the meaning of X cross Y as a CW complex the CW product so X cross Y is a CW product is taken this way once again if you are dealing with finite CW complexes or even finite dimensional CW complexes then you do not need this extra definition because this is finite dimension this is finite dimension say this is m dimension n dimension you will stop at m plus n dimension m plus n dimension skeleton is obtained by m plus n minus 1 dimension skeleton therefore there is no need to redefine the topology by using this okay so this is an easy observation here so the new this redefining the topology is a necessity only when infinite dimensional spaces are enough okay and quite often that is the case therefore we have to study this infinite dimensional case properly and that will be the gist of whatever comes next alright so before crossing further let me examine one more interesting example instead of S1 cross I now I will consider S1 cross S1 the torus once again take the simplest CW structure on S1 on both sides namely 1 0 cell and 1 1 cell on both sides then as usual of course you can think of S1 as a subset of C okay unit vectors or unit complex number and S1 cross S1 is subset of C2 just for fixing notations okay so what is the 0 cell you can declare what you want here I would like to take the minus 1 as a complex number sitting inside S1 as the 0 cell and the characteristic map from J because I am using minus 1 to plus 1 as parameter for the 1 cell so phi from J to C take phi t equal to e power pi IIT okay so we now look at the product silver structure on the S1 cross S1 okay so there is one just 1 0 cell namely the point minus 1 plus 1 you see in the case of S1 cross I you had 2 0 cells so here is only 1 on both sides there is 1 here 1 here there is only 1 possibility and that will be minus 1 minus 1 whereas there are 2 1 cells mainly 1 cell here and 0 cell there and interchange 0 cell here and 1 cell there okay so and what are the characteristic maps for that phi 1 of t is first one phi 1 t comma the constant map minus 1 phi 2 t is minus 1 constant and phi t in the second coordinate so this phi 1 and phi 2 t finally there is just 1 2 cell namely phi cross V J cross J which is just e power pi IIT 1 comma e power pi IIT 2 so that I have written down but that is obvious okay once you have that see look at this one this is S1 cross S1 suppose to be whatever so this is e0 and this is e11 okay and then there is another one e12 so this will be e0 cross e0 okay this will be e1 cross e0 and that will be e2 cross e0 or e0 cross e2 then finally e2 is which is e11 cross e12 so this is 2 cell which will be sitting there okay quite weird way to be sitting so this inner circle here I mean this is nothing inner circle this is a round thing but this is not a part of the skeleton this is not any cell there is only 1 0 cell 1 and 2 these 2 are 1 cells and then 1 2 cell so 0 and 2 and 1 so there are only 4 cells you know okay so this is the way you have to just decompose the given space okay automatically you would know when you write down parameterizations the attaching maps so here let us do that and get a nice output okay so it is interesting note that attaching map of this 2 cell trace is the first circle S1 cross i S1 cross 1 then the second circle 1 cross S1 then again the first circle in the opposite direction and again the second circle in the opposite direction so if you denote these elements say S1 cross 1 the class of that and 1 cross S1 in the fundamental group of this S1 union S1 you see this circle union that circle with one single point common so there is a wedge of 2 circles there is a subspace of the torus right on the subspace of the look at the fundamental group of that then what is it happening is the boundary first goes around this one then goes around that this time it comes around the other way around and goes around that way what is just vacation you can just write down what happens to the p1 t comma p2 t right p1 t by i t by i t but on this one how it is sitting in S1 cross S1 you can work out t power i mean c cross c or there is another method I will tell you so first think of this as the loops in their class of the loops okay if you S1 cross 1 and 1 cross S1 they are X and Y are the same then the loop that is attaching attaching loop is nothing but XY X inverse Y inverse in the fundamental group of S1 edges S1 okay so this is the picture you all know that the torus can be got by attach by identifying this edge with this this edge with this edge and this edge with this edge of course when you identify the arrow is on the other side here here the arrow is on the other side upward okay when you do that this becomes your S1 cross 1 along with that that is also S1 cross 1 that will become 1 cross S1 but now look at this one the boundary of this square you can trace it from here to here to here to here to here this is going to be the boundary of the two cell that I am going to attach attaching map what is the attaching map first it is this one let us call this X that is what I have done then it is Y but now X is this way so when you are tracing this way it is X inverse similarly Y is this way when you are tracing this way it is Y inverse so when you draw the picture on the mother's face of which these are quotients everything will be very clear so this is the lesson you have to learn so this is XY X inverse so when you have attaching XY X inverse we have done in the first part that the fundamental group gets quotiented by this element XY X inverse which means that you have to take the normal subgroup generated by this element go modulo that that will be the fundamental group of the mapping cone the mapping cone is one cell is being attached to the one skeleton S1 cross S1 which has free free group on two generators that is the fundamental group now go modulo XY X inverse Y inverse which is the same thing as declare X commutes with Y what you get is the free abelian group so pi 1 of S1 cross S1 will be the free abelian group over two generators of course this we know already by another method namely we know that pi 1 of X cross Y is pi 1 of X cross pi 1 of Y therefore pi 1 of S1 cross S1 is pi 1 of S1 cross pi 1 of S1 again which is Z cross Z this we this also we know so the point is when you want to learn something new concept you should check it or you should learn it with something which you already know very well so that you will be sure of your ground so that is one case here returning to the general study let us be sure that we whatever you have described as a CW structure on X cross Y is so given any point X comma Y in X cross Y as a set there is a unique P cell sigma in X and a unique Q cell tau in Y such that X is in the interior of sigma Y is interior of tau why because every CW complex is a disjoint union of its open cells each element will be in one of the open cells so it takes a sigma and tau that would mean that X cross Y is precisely a disjoint union of interior sigma across interior of tau these are subsets of X and Y respectively so X cross the product will be subset of that take the disjoint union these things are all disjoint because in the beginning interior sigma and interior sigma prime two different cells they are disjoint inside X similarly tau tau prime inside Y they are disjoint you take all possibilities then you get the entire X cross Y and not only that what happens to K skeleton K skeleton consists of all cells of dimension less than or equal to K you have to put them together so that is why you have to take union of all P plus Q equal to K X power P cross Y power Q for each zero cell X naught of X if you take X naught cross Y that will be some complex because all those cells will come and previously their boundaries would have been inside that if you take a K skeleton here X naught cross Y power K the K plus one cell which looks like X naught cross some cell will have boundary in this way so these will be sub complexes of X cross Y similarly for every zero cell Y I cannot take arbitrary point here ok remember that you have to take cell zero cell Y naught of Y then X naught cross X cross Y naught will be sub complex the product cell can be thought of as obtained by attaching JP cross JPQ with characteristic maps as products of the two characteristic maps where P and Q range over all possibilities P plus Q equal to K in particular all closed cells of X cross Y are closed and compact subsets of the product space because they are just products of compact sets closed subsets of compact sets closed subsets and compact sets ok so the only major concern is when X and Y are in final dimensional or one of them is in final dimensional ok so let us resolve that then we will be very happy with the product of CW complexes so let X and Y be any two complexes we have the first thing is X cross Y W whatever CW complex structure is there the same thing as take just the the product topology and then retopology is it by using compactly generated subsets so that is the meaning of writing W on the outside remember for any space say Z what is the W Z W is the coindistopology through all the compact subsets of Z I want to say that these two are the same so that by chance if you do not have to write here you can write here then also it is correct do not write X cross Y W without bracket that will be different ok the identity map once you have this X cross Y bracket W to X cross Y is continuous so this is we already know so B is automatic ok once you know why this is true then this is automatic identity map is homeomorphism if you know this product is compactly generated this also we know ok identity map X cross Y W to X cross Y defines the bijection of compact subsets this also we know these all these things generally we have studied so we can apply them to the situation of CW complexes the only thing we have to see is why this is true ok now look at the family F of product cells sigma cross tau a sigma and tau range over all close subsets of X and Y that is a cover for X cross Y and these subsets are compact if you have a sub family of compact sets covering the whole space and give the induced topology from that that will be the same thing as the induced topology from all subsets ok so therefore the co-induced topology X cross Y W from this family is actually finer than the weak topology on X cross Y X cross Y W ok because we have to verify only for a chosen family smaller family if we have smaller family the co-induced topology will be finer we will have more open sets it has to satisfy less number of conditions but equality follows from you have to know why it is equal equality follows from the observation that take any compact subset of X cross Y it is covered by finitely many members of this family there will be finitely many close subsets sigma cross tau for any compact set you know that is covered by finitely many cells and what are the cells they will look like sigma cross tau therefore these two topologies are the same and we have seen that BCD other three things are automatically satisfied in the general case so only this was this has to be seen ok so we still have not come to the case when things are infinite what happens we still do not know whether X cross Y W is equal to X cross Y so that is our next concern it will never happen always so what are the best possibilities what we are going to study so here is a definition which will be a nice condition which will guarantee some kind of equality amongst X cross Y W in X cross Y so what is the condition a CW complex is said to be locally countable if every open cell meets only countably many closed cells let me elaborate on this one take a zero cell it is both open and closed what does it mean it means that all the cells which will hit this one how do they hit by using attaching maps all those cells if you count them it will be finitely many in particular the edges or one cells which are coming out of this zero cell there will be finitely many not only that the two cells may be far away I do not care if they have one boundary point in the given zero cell that will be finitely many so this will happen for every every vertex it will happen for every edge if it happens for every case in Plex that is the meaning of this one so the first remark here is if you place open cell by closed cell then this condition is still true suppose I take this condition every open cell meets only countably many closed cells take a closure of that that is a closed cell it is a larger one it may intersect too many of them no it will also meet only countably many why that is so because the closure of each cell being a compact thing covered by finitely many open cells this is one of the properties that we have seen each finitely many open cells will meet again finitely many sorry countably many closed cells so countable union finitely enough countable sets will be again countable ok whether I put every open or closed here does not matter they are the definitions will be the identical now here is a lemma take any locally countable CW complex ok take every locally countable CW complex every point X is contained in a countable sub complex which is a neighborhood of X in X that it is contained in a countable sub complex is obvious you can just take you know one of the cells containing that that is not a point but that will not be a neighborhood in general you have to have a neighborhood of X in X that means the set should contain an open subset of X and contain the point little X ok so this seems to be some more nontrivial thing we shall see this one next time thank you