Exercise 2. Let X be a topological space. Endow X X X with the product topology. Consider the map f: X→ Xx X, x + (x,x). Its image f(X) is the diagonal Ax = {(x,x) | x = X}.} c) Assume that X is Hausdorff. For every closed subset CCX, show that f(C) C X X X is closed in X X X. d) C 001 shery murrixaMarqes

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