please answer #4 asap

Notation and basic conventions. Throughout let X and Y denote topological spaces, and for a subset A of a topological space denote its closure by A and the set of its limit points by A'. 1. a. Prove that a topological space X is Hausdorff if and only if the set A = {(x, r):x e x} is a closed subset of X x X. b. Suppose Y is Hausdorff, A C X, and f: A - Y is continuous. Prove that if g, h: A - Y are continuous extensions of f, then g = h. 2. Prove or give a counterexample: a. For every collection {A.: a E A} of subsets of X, U A. C U A.. DEA GEA b. For every collection {A.: