Introduction to Topology: Made Easy 

27 dislikes are from flat earthers, because you casually proved the shape of the globe just using topology 😂

you made me understand topology in 22 seconds. I think I heard the actual click in my mind

Awesome video!!! Even I can't tell in words how helpful it is for me.Please make videos about topology of glueing,cutting etc.

The precise claim is that every *_closed_* surface (compact connected no-boundary 2-manifold) is determined by its Euler characteristic *_and_* whether it's orientable or not.

Hey small issue with the video... I think. Continuous deformation l is not a homeomorphism.. It's called a homotopy. A homeomorphism is just a bicontinuous bijection and in general is a much much less demanding map. For example, a trefoil knot and a circle are homeomorphic, but there is no continuous deformation possible between the two. Cheers!

Still donut understand

Wonderfully explained. Thanks a lot!

Topology does not apply only to manifolds in R^n. Do these 'stretching' analogies apply to non T1 spaces? I ask because I am suspicious of 'rubber sheet geometry' being used as a description of topology per se.

This is interesting, it makes me wanna learn topology

Study Group theory and real/complex analysis before touching topology. The concepts in algebra and analysis naturally lead to topology

Jack Li's videos: Music, music, music, music.. TOPOLOGY!!

Hey nice video! I really enjoyed your intuitive explanation. You made it real interesting and good luck bro!!

This is late, but I'm confused about the earth "obviously" being simply connected. If we were coming from the perspective of having never seen space images of the earth, how would we figure out that all loops can be adjusted to a point? Sorry if this is stupid, but I'm stuck on that. I've been listening to math lectures while on a road trip today, so my brain is a bit tired. I came to this video to get an explanation of how a coffee cup is a torus (I kind of get that).

And logical-mathematical psychoanalysis. started from lacan analytic discourse. Thanks for the video!!!!!!

This is the first video of topology I ever watched. Thank you for sparking my interest.

Laughs in blender

This is interesting, it makes me wanna learn clarinet

Hey, can you turn a torus into a kline bottle? Both euler characteristics are 0, but I believe you can’t.

'every surface is homeomorphic to either a sphere, torus, double torus etc..' What about an annulus, double annulus, etc? Toruses contain a 2D hole (the space in the middle) but annuli do not (sorry if incorrect terminology). Surely they are not topologically equivalent? (I'm pretty new to topology but if anyone could explain I'd be really grateful)

Excellent visual demonstration of useful applications! Make more, more, more !! =)

Does this guy have a cold or allergies or something??

It's pronounced, You-ler.

I will now use this knowledge to debate flat-earthers. Earth must be a sphere!

There's a lot of homeomorphism in San Francisco.

"Next time you're out with your topologists friends..." 😂

Two surfaces having the same euler characteristic does not garantee that they are homeomorphic. It is a required condition but it is not sufficient. In general the video is only about orientable surfaces, for which this is true, but there are also non orientable surfaces.

Every surface is homeomorphic to a ball, a donut, an eight or a fidget spinner. Got it

Hi Jack great video. Any chance of and introduction to manifolds? Peter

Its not important to worry about why maths is important. One can assume it isn't and prove it is always.

Aye yo my g big ups man

each bridge, window, dor tunnel, .... i am not quite sure what the euler caracteristic of earth is....

Great tutorial... there’s “a rat” in separate -> separable. )

( mathematical term for a donut 😂)

super .....create more videos like this....with a picturized explanation .....one can easily understand .....next part pls😊 😊

How do you know that Earth is simply connected?

I see some crossovers to Calc 3.

This is a fabulous video. Incredibly clear and helpful. Bravo!

cant stop pretending😭

Why this video is recommended while I'm trying to studying the topic of math?

Finally! A video with simple explanation on the concept of genus!

top

very interesting and straight forward, however I guess the word "verticies" is a wrong spelling

Great video!

Mind-blowing! Quality over quantity (5:00 min)!

That is a bad definition of homeomorphism. What matters is that there is a one to one function that assigns one set to another set. Euler characteristic is only one of an infinite number of choices of such a function.

bro thats so facts

Excellent !

that was a homotopy and the iff statement with euler characteristic doesn’t hold

This explanation provides very good insight. A very good video.

very good!

This is just wrong. You can deform a ring in a circle without cutting nor terring yet they are not homeomorphic. The ring is arch-connected when removing two points and the circle is not.

Wah! I think I got the idea, thanks a lot, much better than reading a book!

easiest explanation found till now great

I am PHD in Topology, and this is the simplest explanation for laymen

dude. this is money. have a donut.

My college needs you as a teacher!

Splendid

Outstanding Dear!!!!!!!!!!!!!!!!1 waow!!!!

This video has saved my masters

@ Jack Li ...what program did you use to create your presentation? Thanks

Awsm..am speechless ..cant use wordz for prase on your presentation on topology

Very cool video, thanks

great video!! thanks a lot

clear and crisp intro to the concept.....

Very insteresting subject. Excellent explanation. Thank you so much!

This is content.

Thanks for the awesome video! Now when my friends talk intuitively about topology, I know what to say.

Very nice video. Thanks a lot :-)

PLEASE PART TWO

Great video - I understand it

Amazing👌🏻

You have a typo at 1:19. It should be vertices. Other than that, thank you for the introduction.

No words!!!

Awesome

I like the concept of deformation in telling a lot about what the future is preparing for us to discover

Thank you very much for sharing your knowledge freely. In my religion this has a big reward for you from Allah. Thank you again.