Very nice lecture Sir. I was reading open mapping theorem in functional analysis where in its proof, we use Baire category theorem. So I was looking concept behind baire theorem. And this lecture ends all my search. I got clear concept of baire th. Thanks a lot sir for this video.
Each and every moment of this lecture is precious. I am totally amazed. I was so absorbed in it that I did not notice how 57:19 min passed. 👌👌👌👌👌👏👏🙏🙏🙏🙏🙏🙏
Very good lecture....Most of the lectures speak about how to go from step n-1 to step n.....very few gives us intuition...Your lecture give students a very good amount of intuitive idea....Through your lectures we learn to enjoy Mathematics...Thank you for all your efforts...Eagerly waiting for the next series of Lectures
There are other series of lectures: Real Numbers, Sequences, Continuity, Uniform Continuity, Group Actions,.. Start from the beginning even if you are very confident. Watch any video not more than 20-30 minutes, stop at a P-R-P. Resume it after sometime. Or, use them as bedtime watches than the soap-operas/TV serials. Do not strive to remember, be with the flow of thinking, think along with me. You will be amazed how this transforms you in about a month's time.
Thank you sir for taking into different world after long time especially during this lockdown. I have completely involved in the proof and not felt like in watching video. Beautifully constructed the proof.
Thank you so much sir..I request you to upload videos on this theorem..I am very much excited after seeing your videos..you also told me to read your books..I read all the results from your books..I never think about geometry of metric space..but after seeing the proof of baire category theorem from your books by diagram..no words to express my excitedness...I think you are one of the best mathematician in the world...
Thank you sir...you provide the idea why should we modify open balls to closed balls in the proof...that's was awesome...it'll be better if you share some lectures on elementary topics of algebraic topology...
@@kumarhcu yes sir now i fully watched the video and enjoyed mostly 1st 30 minutes where you grow the motivation that why we need category th and the approach how to proof the result .........Thank you very much sir for this kind of effort for us........
Thank you so much sir. It was a long time wish to learn this theorem properly and now it has been fulfilled. I request you for a separate lecture video on logic sir. (Similar to the Foundation course in MTTS for Level O).
Or ek sir space felling curve curve and cantor function related ek vedio. Sir your book is very good..ham ne AP ki book para he.it is very nice and purpose to develop knowledge
Suppose if there exist such a d then Q cannot be written as a countable union of nowhere dence set but that is not true because Q is countable and it can be written as union of singletons (singletons are nowhere dence in usual metric) sir is this argument correct?
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Very nice lecture Sir. I was reading open mapping theorem in functional analysis where in its proof, we use Baire category theorem. So I was looking concept behind baire theorem. And this lecture ends all my search. I got clear concept of baire th. Thanks a lot sir for this video.
Each and every moment of this lecture is precious. I am totally amazed. I was so absorbed in it that I did not notice how 57:19 min passed. 👌👌👌👌👌👏👏🙏🙏🙏🙏🙏🙏
Thank you very much!
Respected Sir,
Very lucky to get a chance to learn.
Two kinds of training I always enjoy in every lecture:
1. How to learn,
2. How to teach.
Thank you for your words of appreciation.
You are really great sir. 🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏
Thanks a lot
Thank u sir....this is very helpful 🥰
Very good lecture....Most of the lectures speak about how to go from step n-1 to step n.....very few gives us intuition...Your lecture give students a very good amount of intuitive idea....Through your lectures we learn to enjoy Mathematics...Thank you for all your efforts...Eagerly waiting for the next series of Lectures
There are other series of lectures: Real Numbers, Sequences, Continuity, Uniform Continuity, Group Actions,.. Start from the beginning even if you are very confident. Watch any video not more than 20-30 minutes, stop at a P-R-P. Resume it after sometime. Or, use them as bedtime watches than the soap-operas/TV serials. Do not strive to remember, be with the flow of thinking, think along with me. You will be amazed how this transforms you in about a month's time.
@@kumarhcu okay sir🙂
I really enjoyed the video...now the Baire Category theorem is clear to me...thank you sir..you are really great ...🙏🙏🙏🙏
All the best
Sir please explain "Tietze extension theorem"..and "Arzela - Ascoli Theorem"..
exactly sir these two theorem needs so much......
So nicely explained sir.
We did it for locally compact spaces in our mtts programme...
Thoroughly enjoyed the lecture!
Thanks for all the efforts.
🙏🏽
Thanks. All the best.
Thank you sir for taking into different world after long time especially during this lockdown. I have completely involved in the proof and not felt like in watching video. Beautifully constructed the proof.
So nice of you
Thank you so much sir..I request you to upload videos on this theorem..I am very much excited after seeing your videos..you also told me to read your books..I read all the results from your books..I never think about geometry of metric space..but after seeing the proof of baire category theorem from your books by diagram..no words to express my excitedness...I think you are one of the best mathematician in the world...
Thank you very much. I appreciate your excitement.
Keep motivating us for doing pure/abstract mathematics with your videos for .... ❤
I will try my best
Thank you sir...you provide the idea why should we modify open balls to closed balls in the proof...that's was awesome...it'll be better if you share some lectures on elementary topics of algebraic topology...
I am glad that you noticed the subtle point of my exposition. It (Alg.Top.) will be quite a while when I come to it.
Awesome lecture sir 🙏
Thanks and welcome
Thank you sir....i need a lecture on this topic from very earlier and now you uploaded thank you sir......
Watch it completely and then tell us whether you liked it and whether you are confident of the result?
@@kumarhcu yes sir now i fully watched the video and enjoyed mostly 1st 30 minutes where you grow the motivation that why we need category th and the approach how to proof the result .........Thank you very much sir for this kind of effort for us........
Thank you so much sir. It was a long time wish to learn this theorem properly and now it has been fulfilled. I request you for a separate lecture video on logic sir. (Similar to the Foundation course in MTTS for Level O).
Yes, it (Foundations) is also on the cards.
Thank you sir for upload your lecture
Most welcome
Nice sir thank you
Sir please explain arzela asscolli theorem...and related things.please
Sure, soon. But which version? on the compact subset of reals or on any compact metric space?
@@kumarhcu yes sir.actually functional analysis mera best subject he usi kelie sir C[0,1] related,compact set related
Or ek sir space felling curve curve and cantor function related ek vedio. Sir your book is very good..ham ne AP ki book para he.it is very nice and purpose to develop knowledge
@@kumarhcu yes sir
Thank you for the video sir..Sir,Can you to start a similar course on riemannian geometry..
No, perhaps after a year! It is not on my priority list.
Suppose if there exist such a d then Q cannot be written as a countable union of nowhere dence set but that is not true because Q is countable and it can be written as union of singletons (singletons are nowhere dence in usual metric) sir is this argument correct?