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

1. Nov 3, 2008

Unassuming

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) $$\subseteq$$ 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.

Last edited: Nov 3, 2008