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Let X, Y be metric spaces, with Y complete. Let S ⊂ X and let f...

Let X, Y be metric spaces, with Y complete. Let S ⊂ X and let f : S → Y be uniformly continuous. (a) Suppose p ∈ S closure and (pn) is a sequence in S with pn → p. Show that (f(pn)) converges in y to some point yp.

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