# Solving a problem involving the closure of 2 sets

• Sep 22nd 2010, 08:27 AM
thedoctor818
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. :(
• Sep 22nd 2010, 12:14 PM
tonio
Quote:

Originally Posted by thedoctor818
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