Question: Problem 31. Let X be a metric space. (a) Prove that the following are equivalent: (1) X is compact. (ii) For any collection of closed

Problem 31. Let X be a metric space. (a) Prove that the following are equivalent: (1) X is compact. (ii) For any collection of closed subsets .# with the finite intersection property, we have (cc.2z C # 0. (b) Let {x,} be a convergent sequence with limit x. Prove that C={x, : neN}U{x}. is compact

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