Proof for Unions and Intersections of Open Sets | Real Analysis
We prove the union of a collection of open sets is open, and the intersection of a finite collection of open sets is open. To do this, we use basic set operation properties and the definition of open sets. #RealAnalysis
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Пікірлер: 14
Just started this topic in my analysis course. great vid as always
Great video as always!
@WrathofMath
Жыл бұрын
Thank you!
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?
Another banger by Wrath Of Math
@WrathofMath
Жыл бұрын
Bangers all day everyday! Really want to get my momentum back on the Real Analysis playlist.
Well explained for me
@WrathofMath
Жыл бұрын
Awesome, thanks for watching!
Arigato :3
Why does the intersection have to be of a finite collection ?
@sHexuality
5 ай бұрын
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
@user-cp3tm2nx5l
5 ай бұрын
@@sHexuality AH that makes so much sense, thanks a lot !
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