prove the following statements each part is worth 5pt a let rn be a co
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Prove the following statements. [Each part is worth 5pt (a) Let {rn} be a converging sequence in a metric space X and let x € X be its limit. Use
the definition of compactness to show that the set {x}U{xn} is compact. (b) Show that a subset of a metric space X is closed if and only if its intersection with every compact subset of X is closed.