I love for u to do this video Let f: X maps Y be a function, not necessarily continuous, between two topological spaces. Let ℬ be a basis for y, and suppose that f inverse of B is open in X for all B in ℬ. Then prove that f is continuous.
take the set A_n= (-1/n,1/n), then the infinite intersection of all A_n such that n is a (non-zero) natural number is the set {0}. But there is no neighborhood of 0 such that this neighborhood is contained within the set {0}, so it is not open
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You explain this well. Good job
Thank you!
Just started this topic in my analysis course. great vid as always
Great video as always!
Thank you!
I love for u to do this video Let f: X maps Y be a function, not necessarily continuous, between two topological spaces. Let ℬ be a basis for y, and suppose that f inverse of B is open in X for all B in ℬ. Then prove that f is continuous.
Another banger by Wrath Of Math
Bangers all day everyday! Really want to get my momentum back on the Real Analysis playlist.
Thankkkk youuuu soooo muchhhh 😭😭😭💓💓💓
Well explained for me
Awesome, thanks for watching!
these videos are amazing i would wanna ask for some on cauchy criterion of series🙏🙏
Is union of finite open sets open?
Is intersection of infinite open sets open?
Why does the intersection have to be of a finite collection ?
take the set A_n= (-1/n,1/n), then the infinite intersection of all A_n such that n is a (non-zero) natural number is the set {0}. But there is no neighborhood of 0 such that this neighborhood is contained within the set {0}, so it is not open
@@sHexuality AH that makes so much sense, thanks a lot !
Arigato :3
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