2. Let f and g be continous mappings on a metric space X into a metric space Y and E be a dense subset of X (a) Prove that f (E) is dense in f (X) (b) If f (p)-g (p) for all p E, then f (p) g (p) for all p eX 3. Let (an) be a sequence in a metric space X. (a) Prove if X is compact, then xn → x if and only if every convergent subsequence of {z») converges to 1. (b) Find a counterexample showing that (a) may not hold when X is not compact.

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