Let f and g be continuous functions from a topological s

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Let f and g be continuous functions from a topological space X into a Hausdorff topological space Y.( you may assume tha

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Let f and g be continuous functions from a topological space X into a Hausdorff topological space Y.( you may assume that X and Y are metric spaces if you wish.? a. Prove that the set C={x element of X: f(x)=g(x)} is closed in X. b. let A be a subset of X and assume that f(a)=g(a) for all a element of A. Prove that f(x)=g(x) for all x in the closure of A.

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