Manifolds 15 | Regular Value Theorem in ℝⁿ

[@StratosFair]

I really like learning about manifolds, I'm looking forward to the next videos ! :)

[@roxanabusuioc5957]

I've been confused by this theorem the whole academic year and I am so happy I finally got the intuition for it!!! Immensely grateful ✨

[@brightsideofmaths]

Happy to help! And thanks for the support :)

[@malawigw]

Manifolds make my day! Thanks

[@PunmasterSTP]

Regular value theorem? More like "Really good videos; more people should see 'em!"

[@فريدريكنيتشه-ع1ش]

thanks

[@ceyhunaliyev8287]

good luck

[@brightlin777]

I have a question : Is topology primarily concerned with studying these specific topological spaces called manifolds (i. e. manifolds are more useful spaces than others) or are manifolds just a part of it ? Because most topological spaces I can think of now (and visualize) are manifolds.

[@brightsideofmaths]

No, manifolds are already very special and rich topological spaces. However, that is the reason that they are very important.

[@angelmendez-rivera351]

Topology is not primarily concerned with studying manifolds. However, this particular video series is concerned primarily with manifolds. This is why the series is titled "Manifolds" and not titled "Topology."

[@MdMaazheralam]

wow this is very interesting video ❤️❤️❤️❤️ ..in semester 4msc manifolds is going on ❤️❤️❤️

[@꿀리리-w6s]

thanks😄

[@brightsideofmaths]

You're welcome!

[@id-ic7ou]

At 6min you said that the rank is well defined because the transition maps are différentiable. I can see that the rank exits for every charts but is it trivial to see that the rank has in fact the same value for all charts?

[@brightsideofmaths]

Thanks for the question. You have to put in the transitions maps to prove this claim :)

[@tensorfeld295]

😀😀

[@changhanchao9654]

ok so this is not the end right..

[@brightsideofmaths]

No, it's not the end :)

[@Sidionian]

Hey mate... Where is the section on differential forms and generalized stokes Theorem you promised...?

[@brightsideofmaths]

Hey mate! It's in production :)

[@Sidionian]

@@brightsideofmaths hurry up mate hahaha 😇😁 Thanks ✌🏼 P. S. how many more videos to go?

[@brightsideofmaths]

@@Sidionian Yeah, manifolds videos really take time because it's not easy to explain it in a tidy way. I plan around 30-40 videos in total here.

[@Sidionian]

@@brightsideofmaths wow... That's going to take a long time at this rate... Hopefully you can manage to catch up a bit, because this is one of the important concepts not so well explained on KZbin... I'm sure your popularity will increase significantly if you can get these videos out... Especially on differential forms and Stokes...

[@brightsideofmaths]

@@Sidionian I upload 2-3 videos each week. The manifolds series will get new ones soon.