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 February 18th, 2009, 11:58 AM #1 Newbie   Joined: Feb 2009 Posts: 1 Thanks: 0 Closed/Open sets Hey guys. I'm stuck on a problem and I need some direction/help on how to solve it: Prove that a set U c M is open IFF none of its points are limits of its compliment. Thanks!
 February 18th, 2009, 03:58 PM #2 Senior Member   Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0 Re: Closed/Open sets Hint: A set $U\subset M$ is open iff for every point $x\in U,$ there exists an $\varepsilon$ such that the ball $B(x,\varepsilon)\equiv\{y|y-x||<\varepsilon\}" /> lies entirely in U.

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