Editing Finite intersection property (section)

=== Compactness ===
The finite intersection property is useful in formulating an alternative definition of [[Compact space|compactness]]: 

{{math theorem | math_statement =A [[Topological space|space]] is compact if and only if every family of [[Closed set|closed subset]]s having the finite intersection property has [[#non-empty intersection|non-empty intersection]].{{sfn|Munkres|2000|p=169}}<ref>{{planetmath| urlname=ASpaceIsCompactIffAnyFamilyOfClosedSetsHavingFipHasNonemptyIntersection| title=A space is compact iff any family of closed sets having fip has non-empty intersection}}</ref>}}

This formulation of compactness is used in some proofs of [[Tychonoff's theorem]].