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

  1. Nov 3, 2008 #1
    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.
     
    Last edited: Nov 3, 2008
  2. jcsd
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