please answer #3 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):rex} 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 9, h: A - Y are continuous extensions of f, then 9 = 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 { Aa; ( ( A} of subsets of X, U An ? U Aa. GEA GEA 3. Find the closure of the subset A = ((x, y): x e [0, 1] \\ Q and (x - ;)3 + (1 - ;) = 16) of the ordered square /2 = [0, 1] x (0, 1] (in the dictionary order topology). Justify your answer. Pictorial arguments with explanations are encouraged