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本帖最后由 hbghlyj 于 2023-1-11 14:32 编辑 1) A metric space $(X,d)$ is called sequentially compact if every sequence in $X$ has a convergent subsequence.
If we replace "Cauchy" for "convergent", the restriction is looser:
2) A metric space $(X,d)$ such that every sequence in $X$ has a Cauchy subsequence.
$\Bbb Q\cap[0,1]$ is a metric space that satisfies 2) but not 1) |
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