Question: Suppose that X is a separable metric space which satisfies the Bolzano-Weierstrass Property, that Y is a complete metric space, and that E is a

Suppose that X is a separable metric space which satisfies the Bolzano-Weierstrass Property, that Y is a complete metric space, and that E is a bounded subset of X. Prove that a function f: E → Y is uniformly continuous on E if and only if f can be continuously extended to E; that is, if and only if there exists a continuous function g : E → Y such that f(x) = g(x) for all x ∈ E.

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