About: Finite intersection property

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In general topology, a branch of mathematics, a non-empty family A of subsets of a set is said to have the finite intersection property (FIP) if the intersection over any finite subcollection of is non-empty. It has the strong finite intersection property (SFIP) if the intersection over any finite subcollection of is infinite. A centered system of sets is a collection of sets with the finite intersection property.

Attributes	Values
rdfs:label	Finite intersection property (en)
rdfs:comment	In general topology, a branch of mathematics, a non-empty family A of subsets of a set is said to have the finite intersection property (FIP) if the intersection over any finite subcollection of is non-empty. It has the strong finite intersection property (SFIP) if the intersection over any finite subcollection of is infinite. A centered system of sets is a collection of sets with the finite intersection property. (en)
sameAs	Finite intersection property Finite intersection property
dbp:wikiPageUsesTemplate	dbt:Em dbt:Harvtxt dbt:Pi dbt:Reflist dbt:Collapse_bottom dbt:Collapse_top dbt:Math_theorem dbt:Planetmathref dbt:Families_of_sets
Subject	Set families General topology
gold:hypernym	Nonempty
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Finite_intersection_property?oldid=1061782514&ns=0
Wikipage page ID	365026 (xsd:integer)
page length (characters) of wiki page	8790 (xsd:nonNegativeInteger)
Wikipage revision ID	1061782514 (xsd:integer)
Link from a Wikipage to another Wikipage	Locally compact space Ultrafilter (set theory) Uncountable set Alexandroff extension Bijection Set families General topology General topology Discrete space Pi-system Set (mathematics) Surjective function Trivial topology Closure (topology) Compact space Open set Empty set Filter (mathematics) Filters in topology Image (mathematics) Index set Perfect set Hausdorff space Intersection (set theory) Interval (mathematics) Tychonoff's theorem Subset Total order Mathematics Neighbourhood (mathematics) Nested intervals Rational number Real number
has abstract	In general topology, a branch of mathematics, a non-empty family A of subsets of a set is said to have the finite intersection property (FIP) if the intersection over any finite subcollection of is non-empty. It has the strong finite intersection property (SFIP) if the intersection over any finite subcollection of is infinite. A centered system of sets is a collection of sets with the finite intersection property. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Finite_intersection_property
is Wikipage redirect of	Centered system of sets Centered System of Sets Sfip Strong finite intersection property
is Link from a Wikipage to another Wikipage of	Nonstandard analysis Baire category theorem Banach–Alaoglu theorem Centered system of sets General frame Glossary of set theory De Bruijn–Erdős theorem (graph theory) List of general topology topics List of mathematical abbreviations List of set identities and relations Compact space Compactness theorem Convergence space Countable set Filter (mathematics) Filters in topology Index of combinatorics articles FIP Helly's theorem Inverse limit Krein–Milman theorem Kőnig's lemma Centered System of Sets Markov–Kakutani fixed-point theorem Net (mathematics)
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Finite_intersection_property

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