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February 18th, 2009, 11:58 AM   #1
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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!
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February 18th, 2009, 03:58 PM   #2
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Re: Closed/Open sets

Hint:

A set is open iff for every point there exists an such that the ball |y-x||<\varepsilon\}" /> lies entirely in U.
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