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.