Assume that B is a connected subset of X and B intersects both A and X \ A, for some subset A in X. Prove that B intersects the boundary \ where int(A) is the interior of A.
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Both are disjoint open sets. If that leads at once to a contradiction to B being connected.
Last edited by Plato; February 24th 2009 at 03:30 PM.
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where int(A) is the interior of A.
