5. Choose whether each of the following statements are true or false. (a) If f is a real-valued continuous function on the closed interval [a; b], then f is uniformly continuous. (b) Let (Mi ; di ) metric spaces for i = 1; 2 and f : M1 → M2 be continuous. Then f(U) is open in M2 for all open subset U in M1. (c) Every homeomorphism is uniformly continuous.

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