A Cauchy sequence is convergent it has a convergent subsequence. Actually compact spaces have a much stronger
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Actually compact spaces have a much stronger property than boundedness. A metric space X is totally bounded if, for every r > 0, it is contained in a finite number of open ball Br(xi) of radius r, that is,
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The open balls are said to cover X.
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Let be a Cauchy sequence in a metric space For every 0 there exists such that 2 ...View the full answer
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