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Thread: Boundaries - interior and exterior

  1. #1
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    Boundaries - interior and exterior

    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 \partial A = \overline {A} \ int(A) where int(A) is the interior of A.
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  2. #2
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    Both Int(A)\;\& \;X\backslash \overline{A} are disjoint open sets.
    If \partial (A) \cap B = \emptyset that leads at once to a contradiction to B being connected.
    Last edited by Plato; Feb 24th 2009 at 04:30 PM.
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