Question: Q1. Let f: {X,d) ) (Y, p) be a function. (a) Show that for each A Q Y,f'1{Y A) = X f'1(A). (b)

Q1. Let f: {X,d) ) (Y, p) be a function. (a) Show that for each A Q Y,f'1{Y \\ A) = X \\ f'1(A). (b) Show that f is continuous if and only if for each closed subset F of Y, f'1(F) is closed in X. (You may use, without proof, the open set characterisation of continuity if convenient.)

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