Introduction to Topology. Fundamental Groups. Homeomorphisms

Support me by checking out www.supportukr....
Introduction to Topology. In this video, I will introduce the motivation to study topology. I will talk about topological spaces, continuous maps, homeomorphisms, and what does it mean to be homeomorphic.
If you like the video, please help my channel grow by subscribing to my channel and sharing my videos.
Thank you for watching!
Maksym Zubkov
[e-mail]

[@PunmasterSTP]

Introduction to topology? More like "This has got to be"...one of the best introductory videos I've seen on this topic on KZbin!

[@emperorpingusmathchannel5365]

Thank you so much! I was never able to get a clear grasp of the fundementals of topology without vague analogies and connections to coffee cups. Your video helped me so much.

[@MathForLife]

Yes! I am glad that you liked it:)

[@hyperduality2838]

@@MathForLife Continuous (sphere) is dual to discrete (torus). Classical (smooth) is dual to quantum. Angular momentum in physics is therefore based upon the topology of a torus as it is quantized. Space is dual time -- Einstein. Symmetry is dual to conservation -- the duality of Noether's theorem. Bosons (symmetric wave functions) are dual to fermions (anti-symmetric wave functions). Waves (Bosons) are dual to particles (fermions) -- quantum duality. The fundamental group = equivalence (homotopy) = duality! "Always two there are" -- Yoda.

[@jamesbentonticer4706]

I am glad youtube is starting to recommend these videos to me. I just wish I found it sooner. I love your delivery and the chalk board is awesome. I prefer blackboard over whiteboard almost any day.

[@stanley2696]

It is wonderful to see math, science, literature and all other ambitious youtubers getting more and more popular. You are making a society at least slightly more ambitious. Thank you for this!

[@MathForLife]

Thank you!!:))

[@cyberyetti]

Please continue and complete this series. Thank you.

[@MathForLife]

Okay, thank you!

[@nocomment296]

I watched dr peyman video but was confused as it's my first time studying topology... Thanks I landed here❤️

[@MathForLife]

Thank you for watching 😊

[@robertschlesinger1342]

Maksym, You look rather young, but you present an excellent introduction worthy of teachers far beyond your years. Very interesting, informative and worthwhile video. I look forward to watching your forthcoming videos. Thank you.

[@MathForLife]

Hi Robert, Thank you for your kind words! I really appreciate your feedback. Thanks for watching!

[@WajeehKhan]

Please continue this series, this one was a great intro to Topology.

[@Fetrose]

Super helpful. Big thanks.

[@MathForLife]

Thank you for watching!

[@deeptendusantra670]

This is a great video for introducing topology. A perfect mix of maths and intuition.

[@srsatapathy1618]

I am watching it after two years but i am so happy to get this video on KZbin, it helps a lot.

[@MathForLife]

Thank you for watching!

[@chuckles8519]

You should definitely continue the series - you explain the material very well.

[@MathForLife]

Thanks! I am working on it.

[@leonardocosta3024]

It sounds great! I would very gladly continue watching this series

[@Lakshin01]

I didn't fully understand what you said in the first part, the second, 3rd and 4th part taught me a lot... Thank you 😊

[@MathForLife]

What did not you understanf in the first part? I want to make sure that I will be clear next time.

[@Lakshin01]

@@MathForLife The notations

[@MathForLife]

Oh, the notations will be explained in the future. This is just the way to say that this topological space has this assigned structure.

[@Lakshin01]

@@MathForLife Good then 👍

[@pinop8433]

Very good. When possible, please talk about connections with Feynman diagrams / Mizera, Mastrolia Twisted Cohomology, of course ... for dummies ... Pino.

[@stipepavic843]

very good , suubed!!

[@chinedueleh3045]

Where is the next video please? Really great!!

[@danielvanbelgie5807]

Exellent concise intro! Please keep going, thank you.

[@MathForLife]

Thank you!

[@petergreen5337]

Thank you very much.

[@colaurier2594]

This is incredibly useful ! Thanks !

[@MathForLife]

Thank you for watching!!

[@gucker]

Great overview, thank you!

[@MathForLife]

Thank you!! I will post some cool stuff later:) CW complexes are super fun

[@yueteng2046]

really clear explanation! thank you so much!

[@MathForLife]

Thank you for watching!

[@PRINCEKUMARCHAUDHARY.]

My life Mathematics & Physics.

[@jayeshgangode6006]

Please continue...

[@MathForLife]

Sure.

[@hyperduality2838]

Continuous (sphere) is dual to discrete (torus). Classical (smooth) is dual to quantum. Angular momentum in physics is therefore based upon the topology of a torus as it is quantized. Space is dual time -- Einstein. Symmetry is dual to conservation -- the duality of Noether's theorem. Bosons (symmetric wave functions) are dual to fermions (anti-symmetric wave functions). Waves (Bosons) are dual to particles (fermions) -- quantum duality. The fundamental group = equivalence (homotopy) = duality! "Always two there are" -- Yoda. Mind is dual to matter -- Descartes. Concepts are dual to percepts -- the mind duality of Immanuel Kant. "Concepts without percepts are empty, percepts without concepts are blind" -- Immanuel Kant. "The intellectual mind/soul (concepts) is dual to the sensory mind/soul (percepts)" -- the mind duality of Thomas Aquinas.

[@TheNachoesuncapo]

Hi! Why is this channel called math for life???

[@MathForLife]

Life credo:D

[@andresxj1]

Is homeomorphic as isomorphic?

[@MathForLife]

In some sense yes and no, the concept of isomorphism is applied to algebraic structures such as groups. We say that two groups are isomorphic if there exists a bijective homOMorphism between them. Two spaces are homEOMorphic if there exists a bijective continuous map between spaces s.t. the inverse of this map is also continuous. I will show explicit examples later.

[@atiurrahman7907]

What actually topology is! What purpose do the topological space serve? How set is connected to topology?

[@srn-m205-4]

I want you teach Modulo.