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Finite intersection property

In general topology, a branch of mathematics, a family A {\displaystyle {\mathcal {A}}} of subsets of a set X {\displaystyle X} is said to have the finite intersection property (FIP) if any finite subfamily of A {\displaystyle {\mathcal {A}}} has non-empty intersection. It has the strong finite intersection property (SFIP) if any finite subfamily has…

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Definition

Examples and non-examples

Relationship to π-systems and filters

Applications

General sources

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Map overview Semantic statistics

Finite intersection property

Nodes71
Edges70
Triples31
Avg. degree1.97
Density0.028169
Components1

How this topic connects Entity context

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Finite intersection property

Top relations

related to "Generic" sets and properties · 5
Finite intersection property → Borel, But, If, Lebesgue, The
related to Examples and non-examples · 5
Finite intersection property → For, Fréchet, If, More, The
related to Generated filters and topologies · 5
Finite intersection property → But, Every, FIP, If, The
related to Definition · 4
Finite intersection property → Families, In, Let, Then
related to End-type constructions · 3
Finite intersection property → At, If, More
related to Ultrafilters · 3
Finite intersection property → Let, Then, This
related to Compactness · 2
Finite intersection property → The, Theorem
related to External links · 2
Finite intersection property → Finite, PlanetMath
related to Relationship to π-systems and filters · 2
Finite intersection property → For, The

Important terminology Word statistics

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Important terminology

displaystyle intersection finite property mathcal set family non-empty filter isbn oclc sets uncountable topology perfect subsets general subset open space

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Finite intersection propertyrelated to "Generic" sets and propertiesThe0.60section
Finite intersection propertyrelated to "Generic" sets and propertiesBorel0.60section
Finite intersection propertyrelated to "Generic" sets and propertiesLebesgue0.60section
Finite intersection propertyrelated to "Generic" sets and propertiesIf0.60section
Finite intersection propertyrelated to "Generic" sets and propertiesBut0.60section
Finite intersection propertyrelated to CompactnessThe0.60section
Finite intersection propertyrelated to CompactnessTheorem0.60section
Finite intersection propertyrelated to DefinitionLet0.60section
Finite intersection propertyrelated to DefinitionThen0.60section
Finite intersection propertyrelated to DefinitionIn0.60section
Finite intersection propertyrelated to DefinitionFamilies0.60section
Finite intersection propertyrelated to End-type constructionsIf0.60section

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    Min side: 3
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