(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that cl(U^A) = cl(U^cl(A)).

2. Relevant equations

Theorems...

1.) cl(U^A) [tex]\subseteq[/tex] cl(U)^cl(A)

2.) cl(A)=cl(cl(A))

3. The attempt at a solution

My proof so far,

Let x be in cl(U^A). From #1, then x is in cl(U)^cl(A). From #2, x is in cl(U)^cl(cl(A)).

I am stuck there. I feel like I am one hair away from finishing but cannot.

EDIT: I realized I need to use neighborhoods for this proof. I am currently working on it and I think I might have something.

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# Homework Help: Cl(U ^ A) = cl( U ^ cl(A) )

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