The Closure of a Set is Closed || Metric Spaces Proof

[@yonatankarni8867]

thank you very much, you explained very well!

[@SequinBrain]

I'll finish watching this later, but right off the top, this is what I didn't get about real analysis. I'll also guess that you'll do a far better job of defining the terms than my class did. thx for your tremendous efforts into this subject.

[@ChristopherEvenstar]

I'm trying to learn some stuff. It helped me. Thank you.

[@Eis461]

Helpful

[@TheMathSorcerer]

Glad it helped!!

[@persistenthomology]

Pretty much follows immediately from the definition. The closure is the smallest closed set containing that set, and since the closure of Y contains itself, and is also closed, therefore the closure of the closure of Y is just the closure of Y.

[@TheMathSorcerer]

ya that is not how it is defined here

[@mzarinchang3744]

Excuse me but shouldnt it be like this:the intersection of punctured neighbprhood of X and Y must be nonempty?