please answer #1 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, x): 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