Casuals: *homomorphism* Dr P: *homeomorphism* I've waited for this for a long time - it's quite the treat.
@jrm61146 ай бұрын
he said that they are different
@naturemeets3 жыл бұрын
WoW !, Thanks, Dr. Peyam. " NEVER ENDING LEARNING"
@izaakvandongen74043 жыл бұрын
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".
@francaisdeuxbaguetteiii73163 жыл бұрын
topology is one of my favourite subjects.
@francaisdeuxbaguetteiii73163 жыл бұрын
What the hell happened here
@AmjadKhan-dj8lj2 жыл бұрын
@@francaisdeuxbaguetteiii7316 Also my favorite subject... Please share your Whatsapp no.
@gmjammin4367 Жыл бұрын
Okay Adam
@francaisdeuxbaguetteiii7316 Жыл бұрын
@@gmjammin4367 who is adam
@carterwoodson88183 жыл бұрын
@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
@AltinoSantos3 жыл бұрын
A good video. Good selection of properties and examples. Congratulations.
@dabbinrascal79753 жыл бұрын
Yes I’ve been waiting for this!!! Thank you :)
@denifventear6093 жыл бұрын
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!
@BaterWottleDog10 ай бұрын
im learning this to make math jokes in ceramics class
@SebastianBaum-z2l Жыл бұрын
I enjoyed this video really much. You explained it clearly, while you have such an good welcoming attitude. Keep going!
@sostotenonsosjojododahohlo45807 ай бұрын
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!
@drpeyam7 ай бұрын
Thank you so much :3
@umerfarooq48313 жыл бұрын
'Coffee cup is like a donut' well so much for my donut cravings
@f5673-t1h3 жыл бұрын
In short: Homeomorphisms are just relabelling the points and getting the same topology.
@janouglaeser80493 жыл бұрын
Precisely
@krumpy82593 жыл бұрын
I love those "In short" comments, they give further insights.
@nocomment2963 жыл бұрын
I wasn't interested in maths but watching 3b1r bprp and some other KZbin channel including yours has completely changed my view.... Now I want to do MSc in mathematics... It's an interesting subject
@drpeyam3 жыл бұрын
Congratulations :)
@dariushanson314 Жыл бұрын
I did not expect an Animorph’s reference. Excellent video.
@ahmedmghabat79823 жыл бұрын
This guy is a legend!!!
@darrenpeck1562 жыл бұрын
Wow, awesome and concise presentation.
@vardhanshah Жыл бұрын
Great explanation!
@otaviogoncalvesdossantos8623 жыл бұрын
Thank you Dr Peyam!
@ecologypig2 жыл бұрын
crystal clear! thanks!
@Zubair622 Жыл бұрын
You made topology interesting
@samidracula14842 жыл бұрын
a very good video and explanation , thank you very much
@deeptochatterjee5323 жыл бұрын
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?
@drpeyam3 жыл бұрын
Yes, sn goes to s if for all neighborhoods of s there is N large enough such that for n > N, sn is in that neighborhood
@nocomment2963 жыл бұрын
Thanks sir for such explanation
@gandalfthethotful4793 жыл бұрын
Thanks!
@drpeyam2 жыл бұрын
Thank you so much for the super thanks, I really appreciate it!!!
@gandalfthethotful4792 жыл бұрын
@@drpeyam absolutely! I love the way you teach. Less boring and more by example 👍
@FT0293 жыл бұрын
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.
@drpeyam3 жыл бұрын
Continuity and Compactness kzbin.info/www/bejne/bILPZ4emo9Wqeqc
@FT0293 жыл бұрын
@@drpeyam thanks!
@wiloux3 жыл бұрын
maths is just playing with some pâte à modeler after all ;)
@soumyadipdey4733 жыл бұрын
Very nice sir
@aneeshsrinivas90887 ай бұрын
Fun fact, JRPG maps are the same as a donut; not a sphere. This is another interesting example of a homeomorphism.
@drpeyam7 ай бұрын
Interesting!!
@shivaudaiyar25563 жыл бұрын
Thanks for such a great content with love from India
@willnewman97833 жыл бұрын
20:23 Compact subspaces are not always closed subsets, so this proof does not work. Also, the proof cannot work because it is not true that continuous maps from a compact space are homomorphism, one needs the target to be Hausdorff
@dominicellis18673 жыл бұрын
if you were to curve out the real line into a circle does that mean circles are homeomorphic to the real number line and subsequently any interval on the real number line could you also map the xy plane/the complex plane to a sphere mapping x to a circle generated by theta and y to the semi circle generated by angle psi?
@Apollorion3 жыл бұрын
So far as I understood it... - The real line has two open ends, but a plain circle hasn't, so they aren't homeomorphic. - If from the plain circle you'd take away a single point though, what'd be left of the circle would be homeomorphic with a line. - Those semi circles need to be open ended, too. So the complex plane won't be homeomorphic with the full surface of a sphere. The way of projection you propose leaves open the poles, as shared end points of the semi circles, and also doesn't include a continuous curve on the sphere surface connecting these poles and that's nowhere parallel to the equator. If you 'wish' to project the complex plane on the surface of a sphere, I think a sort of Riemann sphere would do better: - where the equator equals the unit-circle, - one pole equals the origin, - the other pole equals infinitely big, which is the point that is not part of the complex plane. - Longitude is just the argument or phase of the complex number. - Latitude is just dependent on the modulus.
@noahtaul3 жыл бұрын
13:28 ...but both (0,1) and [0,1] are open in themselves, so this doesn’t prove they aren’t homeomorphic. You just showed there’s no homeomorphism of R that sends (0,1) to [0,1], which isn’t the same thing. You need the compactness again, or the fact that there are points of [0,1] you can remove and have the remainder be connected, while this is false for (0,1).
@chriswinchell15703 жыл бұрын
Hi Dr., If you find time, can you make a video about the first homology group? Thanks.
@drpeyam3 жыл бұрын
No way haha
@chriswinchell15703 жыл бұрын
@@drpeyam I’m fairly sure you must have taken algebraic topology and you took it more recently than I because you’re still suffering from ptsd.
@FloduQ3 жыл бұрын
Is it enough to find one homeomorphism f, so that M and N are homeomorphics ? or do we have to say they are homeomorphics for the specific homeomorphism f ?
@drpeyam3 жыл бұрын
One is enough
@isobar58573 жыл бұрын
Well you may not know the the difference between a donut and a cup of coffee but I do...I can eat a donut . Did I pass the test...it was a test, wasn't it ? Sorry for the levity...I gave up on maths after calculus 3. Have a good day sir.
@aurangzeb57353 жыл бұрын
Sir at 0:43 you said that in homeomarphism the function can be from one matric space to another space and at 3:20 you said topology does not see distances. My question is, metric spaces cares about distances so how can we take Metric space as a function in homeomarphism definition?
@dariushanson314 Жыл бұрын
I recommend Munkres Topology for this. Metric spaces are how topological spaces are constructed, and if the inverse of a bijective mapping from one topological space to another is continuous, you have yourself a homeomorphism.
@SS-ld2hk3 жыл бұрын
does (0,1) homeomorphic to R imply that any interval in R is homeomorphism to R
@drpeyam3 жыл бұрын
I think so, at least any open one
@Happy_Abe3 жыл бұрын
Animorph fans represent!
@anchalmaurya23722 жыл бұрын
Sir, 1/2x is not continuous at 0 but apne [0, 2] liya h?
@drpeyam2 жыл бұрын
?
@aneeshsrinivas90882 жыл бұрын
is there a special name for homeomorphisms which are uniformly continuous?
@drpeyam2 жыл бұрын
unimorphisms
@ekadria-bo4962 Жыл бұрын
By the definition, i wonder: Is R^N Homeomorphic to any interval?
@drpeyam Жыл бұрын
No if n >= 2 because if you remove a point from R^n it’s still connected but if you remove a point from an interval it becomes disconnected
@ekadria-bo4962 Жыл бұрын
@@drpeyam i wonder now. What its still true in R^1 and 2 ?
@narutosaga124 жыл бұрын
11:50 how is it that it is both not homeomorphic and homeomorphic at the same time?
@drpeyam4 жыл бұрын
No they are not homeomorphic. If I said they are, I misspoke
@aneeshsrinivas90882 жыл бұрын
Imagine being able to transform any object into any other object as long as they are toplologically homeomorphic in real life(like for example being able to transform a torus into a coffee mug)? How would that be as a superpower ?
@drpeyam2 жыл бұрын
Not very effective…
@Tomaplen3 жыл бұрын
Will Lord Peyam have differential geometry videos on 2021? Would be amazing
@drpeyam3 жыл бұрын
I’m planning on doing a miniseries on differential forms, sometimes later this year
@aneeshsrinivas90882 жыл бұрын
But is there an explicit formula to go from a coffee cup to a donut?
@drpeyam2 жыл бұрын
I bet
@Caleepo3 жыл бұрын
Isnt homeomorphism the same as isomorphism ?
@mikhailmikhailov87813 жыл бұрын
In the category of topological spaces it is. The notion of isomorphism is that you can exactly match two objects and their structure, whatever the structure in question might be.
@Caleepo3 жыл бұрын
@@mikhailmikhailov8781 aight thank you for your answer, But is there a case in which they are actually different ?
@mikhailmikhailov87813 жыл бұрын
@@Caleepo isomorphism is just a generic term for any sort of equivalence between mathematical objects.
@lacasadeacero3 жыл бұрын
The morphism Is something new. Like Stokes theorem. I think we'll find a profound use.
@dgrandlapinblanc2 жыл бұрын
Ok. So (f)-1 is continuous on the circle of radius 1 to the (0,2pi] because she's one to one and not onto sorry. Thank you very much.