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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- February 24th 2009, 02:02 PMalakazamBoundaries - 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 \ where int(A) is the interior of A.

- February 24th 2009, 02:57 PMPlato
Both are

**disjoint open sets**.

If that leads at once to a contradiction to B being connected.