1. The problem statement, all variables and given/known data As the title says 2. Relevant equations Definitions of "open" and "closed" 3. The attempt at a solution Suppose a finite set S is not closed. Then Sc is not open, and there exists an element x of Sc, so that for all µ > 0, either x + u, or x - u, is an element of S. Hmmm ... Where do I go from here? I need a springboard.