Prove that every compact metric space is complete
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A set K is compact if and only if every collection F of closed subsets with finite intersection property has ⋂{F:F∈F}≠∅. A metric space (X,d) is complete if and only if for any sequence {Fn} of non-empty closed sets with F1⊃F2⊃⋯ and diam Fn→0, ⋂∞n=1Fn contains a single point
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