1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?