(a) If A and B are disjoint closed sets in some .... 1. The problem statement, all variables and given/known data (a) If A and B are disjoint closed sets in some metric space X, prove that they are separated. (b) Prove the same for disjoint open sets. (c) Fix p in X, ∂ >0, define A to be the set of all q in Z for which d(p,q) < ∂, define B similarly, with > in place of <. Prove that A and B are separated. 2. Relevant equations Triangle inequality, definitions of open and closed sets 3. The attempt at a solution Give me some hints to finishing part (c).