View source for Equivalent statements to compactness of a metric space/Statement

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==Statement of theorem==
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Given a [[metric space]] {{M|(X,d)}}, the following are equivalent{{rITTGG}}<ref group="Note">To say statements are equivalent means we have one {{M|\iff}} one of the other(s)</ref>:
# {{M|X}} is [[compact]]
# Every [[sequence]] in {{M|X}} has a [[subsequence]] that [[convergent (sequence)|converges]] ({{AKA}}: having a ''convergent subsequence'')
# {{M|X}} is [[totally bounded]] and [[complete metric space|complete]]<!--
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==Notes==
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==References==
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{{Theorem Of|Metric Space}}
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