Question: Let X be a metric space. a) Prove that if E X is compact, then E is sequentially compact (see Exercise 10.1.10). b) Prove

Let X be a metric space.
a) Prove that if E ⊂ X is compact, then E is sequentially compact (see Exercise 10.1.10).
b) Prove that if X is separable and satisfies the Bolzano-Weierstrass Property, then a set E ⊂ X is sequentially compact if and only if it is compact.

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