please answer #2 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 = {(r, I):I 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 H 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.. GEA GEA b. For every collection {A.:a E A} of subsets of X, U A. 2 U A.. GEA GEA