View source for Every sequence in a compact space is a lingering sequence

: '''Note: ''' this page is taking about a [[metric space]] not a [[topological space]] (at least at this time)
{{Todo|Does this apply at all to topological spaces? (Maybe, but with adaptation, as open balls do not exist in general top. spaces)}}
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==[[Every sequence in a compact space is a lingering sequence/Statement|Statement]]==
{{:Every sequence in a compact space is a lingering sequence/Statement}}
{{Note|Note that such an {{M|x}} exists, suggesting the space is complete. See [[Equivalent statements to compactness of a metric space]] for information}}
==[[Every sequence in a compact space is a lingering sequence/Proof|Proof]]==
{{:Every sequence in a compact space is a lingering sequence/Proof}}
==See also==
* [[Lingering sequence]]
* [[Compactness]]
==References==
<references/>
{{Theorem Of|Metric Space|Real Analysis|Functional Analysis}}