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prove: Any nonempty, compact, totally disconnected metric space without isolated points is homeomorphic to the Cantor set.

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 voting to close because this is a standard exercise – Andreas Blass Jul 9 2011 at 14:46
mathoverflow.net/howtoask mathoverflow.net/faq#whatnot – Yemon Choi Jul 9 2011 at 15:32
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 If it were rephrased to be a reference request instead of a command, it might have gotten a much nicer reception. I will say however that it is not just a standard exercise, but a result due to Brouwer. There are probably quite a few proofs. One would be a back-and-forth equivalence proof for countable atomless Boolean algebras. – Todd Trimble Jul 9 2011 at 21:31

closed as too localized by Willie Wong, Andreas Blass, Qiaochu Yuan, Bill Johnson, Charles Siegel Jul 9 2011 at 15:07

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