Math, asked by csaranyasaravanan, 3 months ago

Prove that every compact metric space is complete

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Answered by Anonymous
2

Step-by-step explanation:

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

Answered by Anonymous
1

Answer:

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Step-by-step explanation:

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