What is a Homeomorphism

Is there a difference between a donut and a cup of coffee? It turns out the answer is no! In this video, we'll define the notion of homeomorphism and see why those two objects are homeomorphic. Enjoy!

[frozenmoon]

Casuals: *homomorphism*
Dr P: *homeomorphism*

I've waited for this for a long time - it's quite the treat.

[carterwoodson]

@5:16 Remembers pate a modeler but not play-doh that was excellent!

Ive heard rubber sheet geometry as well, would say "modelling clay" if wanting to avoid the brand name haha

[izaakvandongen]

At 11:00, it certainly is possible to remove a point from that interval without disconnecting it. Just take an endpoint! I think the more usual topological invariants used here include "can remove two points without disconnecting it" or "the number of points you can remove that do not disconnect it" or "the number of points you can remove that do disconnect it".

[naturemeets]

WoW !, Thanks, Dr. Peyam. " NEVER ENDING LEARNING"

[umerfarooq]

'Coffee cup is like a donut' well so much for my donut cravings

[sostotenonsosjojododahohlo]

Dr. Peyam, you are one of the greats on math youtube. I am studying topology right now and some concept can be hard to grasp. Thank you for making videos like this, it really helps! Also you seem like such a fun guy to be around, the energy you give off is amazing. Keep up the good work!

[SebastianBaum-zl]

I enjoyed this video really much. You explained it clearly, while you have such an good welcoming attitude. Keep going!

[denifventear]

You wouldn't believe it but I had to learn and apply this notion in literature for a project haha... So thanks for making it easy enough for me to understand!

[AltinoSantos]

A good video. Good selection of properties and examples. Congratulations.

[dabbinrascal]

Yes I’ve been waiting for this!!! Thank you :)

[dariushanson]

I did not expect an Animorph’s reference. Excellent video.

[francaisdeuxbaguetteiii]

topology is one of my favourite subjects.

[nocomment]

I wasn't interested in maths but watching 3b1r bprp and some other YouTube channel including yours has completely changed my view....
Now I want to do MSc in mathematics... It's an interesting subject

[darrenpeck]

Wow, awesome and concise presentation.

[samidracula]

a very good video and explanation, thank you very much

[FT]

I really like all the motivating examples you give (e.g. the continuous bijection whose inverse isn't continuous)!
I am a little curious about the proof of the property at 9:14.

[f-th]

In short: Homeomorphisms are just relabelling the points and getting the same topology.

[shivaudaiyar]

Thanks for such a great content with love from India

[deeptochatterjee]

I don't know much about topology, is there a way to define the limit of a sequence in a topological space without a metric?

[chriswinchell]

Hi Dr., If you find time, can you make a video about the first homology group? Thanks.