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Thread: Solving a problem involving the closure of 2 sets

  1. September 22nd 2010, 07:27 AM #1
    thedoctor818
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    Solving a problem involving the closure of 2 sets

    I need to proof that: \overline{A \cap B}\subseteq \overline{A} \cap \overline{B}. Any help is greatly appreciated. Sorry, I am having a bit of trouble with my tex skills on this one.
    Last edited by Plato; September 22nd 2010 at 11:26 AM. Reason: LaTeX Fix
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  2. September 22nd 2010, 11:14 AM #2
    tonio
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    Quote Originally Posted by thedoctor818 View Post
    I need to proof that: \overline{A /cap B}\subseteq \overline{A} \cap \overline{B}. Any help is greatly appreciated. Sorry, I am having a bit of trouble with my tex skills on this one.

    Let x be an accumulation point of A\cap B\Longrightarrow \exists \{x_n\}\subset A\cap B\,\,s.t.\,\,x_n\xrightarrow[n\to\infty]{}x , so...

    Tonio
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