you are the greatest teacher ever at linking intuition with rigorous definitions. I can truly see WHY people defined a concept in a certain way. That is very good because it is the most lacking part of the book Topology Without Tears!
I just started on this, but I have to agree with other commenters that this lecturer breaks the taboo that so many books on math seem to have on asking "Why are we doing this?", the question that is the key to all motivation. Thanks!!
This video is awesome! The excitement you have while explaining the stuff really inspires me. I know I will not need this stuff for the rest of my life, but you are triggering some kind of intereset in this topic. Thanks to people like you, students can understand such abstract math!
I really enjoyed your playlist on group theory so this is very welcomed. However, I cannot find any playlist of yours named Topology. What videos are supposed to be included in the playlist that you are referring to in this video?
i can tell you that there is a specific use of topology. it's the reason i come here and it WILL be practically useful for my career. it's used in robot motion planning to understand and represent configuration space. thank you sir for this extremely clear video.
Tks for your videos so much! The best explanation about topological space I've ever heard. This motivates me. I'm studying about measure theory and I don't know intuitive interplay between topology and measure theory. What is the role of topology in measure theory?
@@bjoernogthomas Okay, I didn't know that. With an empty set in your name you surely must know what you're talking about :-) Wikipedia is confirming it. Thanks!
Around 23-24 minute. If we intersect two subsets, and we get an empty subset, does this satisfy the intersection condition for topology? Are these two subsets then in the topology?
I think you've got the if and then mixed up. If two subsets are in tau then their intersection is also in tau. If their intersection is empty then the empty set is already there in tau, so the only real thing to look for is every non-empty intersection must be in tau. What you are doing is reversing the if and then- "if the intersection of two subsets is in tau then both the subsets are in tau"- which is not what the axiom says. I hope I've made myself clear.
It is not thta pure mathematicians insist that empty set and the whole set need to be in the topological space, it because of the unions and intersections. I hope you understand.
you are the greatest teacher ever at linking intuition with rigorous definitions. I can truly see WHY people defined a concept in a certain way. That is very good because it is the most lacking part of the book Topology Without Tears!
I just started on this, but I have to agree with other commenters that this lecturer breaks the taboo that so many books on math seem to have on asking "Why are we doing this?", the question that is the key to all motivation. Thanks!!
you deserve a prize for explaining this!
I finally understand what a topological space is! Thank you so much!
This is really a great explanation, one of the best I have seen!
great,may allah give u alot of happines for this good act and try to creat a helpful idea& emotoin
Indeed a good teacher this will help me alot in my examination come April
Thanks a ton, for being so patient and intuitive 🙏
This is helping me understand the axioms I found in a Japanese textbook that does not explain the motivations behind them. Thank you.
Awesome explanation
Awesome! Thanks for posting this! I need to prepare for next semester as I heard topology is the hardest undergraduate class in maths.
This video is awesome! The excitement you have while explaining the stuff really inspires me. I know I will not need this stuff for the rest of my life, but you are triggering some kind of intereset in this topic. Thanks to people like you, students can understand such abstract math!
Great Work.. may ALLAH give u alot of happiness for this effort
Any reason you haven't created a playlist for these topology videos? Just so its easier to fond which one comes next.
There is a playlist
Nevermind, I think you're right
I like your style of presentation, this is quite good.
enjoyed the topic.. thanks
I really enjoyed your playlist on group theory so this is very welcomed. However, I cannot find any playlist of yours named Topology. What videos are supposed to be included in the playlist that you are referring to in this video?
good!
this is gold.
i can tell you that there is a specific use of topology. it's the reason i come here and it WILL be practically useful for my career. it's used in robot motion planning to understand and represent configuration space. thank you sir for this extremely clear video.
Is a topological space necessarily unbounded by definition??
Very very specific and easy to understand! A little bit verbose, but it does not matter.
Thanks a lot. Can you suggest some good books on Topology?
www.thriftbooks.com/w/topology-of-3-manifolds-and-related-topics_daniel-silver/1902797/item/35494619/?mkwid=%7cdc&pcrid=448963509244&pkw=&pmt=&slid=&plc=&pgrid=104673973815&ptaid=pla-926982115650&gclid=EAIaIQobChMIyODj-6KA7AIVPB-tBh2z_gZkEAQYAiABEgJp1vD_BwE#isbn=0486435873&idiq=35494619
Do you follow a textbook with this series?
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Tks for your videos so much! The best explanation about topological space I've ever heard. This motivates me. I'm studying about measure theory and I don't know intuitive interplay between topology and measure theory. What is the role of topology in measure theory?
thank you for a class video
U_2.1, U_pi on 27:19 it is just some kind of "names" of U?
maybe with Integral
what does U_2.1 means?
damn you're good
Understood so far..
@ 19:00: The symbol for an empty set has nothing to do with the Greek letter phi !
Jacob van Dijk Noticed too. It’s the capital of the danish letter ‘Ø’
@@bjoernogthomas Okay, I didn't know that. With an empty set in your name you surely must know what you're talking about :-) Wikipedia is confirming it. Thanks!
Empty sets can be represented by phi
I can't understand why is topology being defined by those 3 rules? And how those rules works?
great work
i need to textbook
thnks alot sir
Around 23-24 minute. If we intersect two subsets, and we get an empty subset, does this satisfy the intersection condition for topology? Are these two subsets then in the topology?
I think you've got the if and then mixed up. If two subsets are in tau then their intersection is also in tau. If their intersection is empty then the empty set is already there in tau, so the only real thing to look for is every non-empty intersection must be in tau. What you are doing is reversing the if and then- "if the intersection of two subsets is in tau then both the subsets are in tau"- which is not what the axiom says. I hope I've made myself clear.
English accent has it's benifits
Mrigank for sure.
try taking a shot everytime he says set
Thank you.
is it possible ??Toplogy define on empty set?
It is not thta pure mathematicians insist that empty set and the whole set need to be in the topological space, it because of the unions and intersections. I hope you understand.
Hurt my feelings calling the empty set stupid lol
You should get paid for this
Ok
Why are you repeating yourself