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.
Follow Math Help Forum on Facebook and Google+
Both are disjoint open sets. If that leads at once to a contradiction to B being connected.
Last edited by Plato; Feb 24th 2009 at 03:30 PM.
View Tag Cloud