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 $\displaystyle \partial A = \overline {A}$ \ $\displaystyle int(A)$ where int(A) is the interior of A.
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 $\displaystyle \partial A = \overline {A}$ \ $\displaystyle int(A)$ where int(A) is the interior of A.