# Math Help - Boundaries - interior and exterior

1. ## 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.

2. 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.