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finite intersection property : ウィキペディア英語版
finite intersection property
In general topology, a branch of mathematics, a collection ''A'' of subsets of a set ''X'' is said to have the finite intersection property (FIP) if the intersection over any finite subcollection of ''A'' is nonempty. It has the strong finite intersection property (SFIP) if the intersection over any finite subcollection of ''A'' is infinite.
A centered system of sets is a collection of sets with the finite intersection property.
==Definition==
Let X be a set with A=\_ a family of subsets of X. Then the collection A has the finite intersection property (FIP), if any finite subcollection J\subseteq I has non-empty intersection \bigcap_ A_i.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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