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In mathematics, a convergence space, also called a generalized convergence, is a set together with a relation called a convergence that satisfies certain properties relating elements of X with the family of filters on X. Convergence spaces generalize the notions of convergence that are found in point-set topology, including metric convergence and uniform convergence. Every topological space gives rise to a canonical convergence but there are convergences, known as non-topological convergences, that do not arise from any topological space. Examples of convergences that are in general non-topological include convergence in measure and almost everywhere convergence. Many topological properties have generalizations to convergence spaces.

Attributes	Values
rdf:type	Thing
rdfs:label	Convergence space (en)
rdfs:comment	In mathematics, a convergence space, also called a generalized convergence, is a set together with a relation called a convergence that satisfies certain properties relating elements of X with the family of filters on X. Convergence spaces generalize the notions of convergence that are found in point-set topology, including metric convergence and uniform convergence. Every topological space gives rise to a canonical convergence but there are convergences, known as non-topological convergences, that do not arise from any topological space. Examples of convergences that are in general non-topological include convergence in measure and almost everywhere convergence. Many topological properties have generalizations to convergence spaces. (en)
rdfs:seeAlso	Convergent filter Topology Filters
dcterms:subject	Mathematical structures Topology
Wikipage page ID	66374616 (xsd:integer)
Wikipage revision ID	1087341221 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian closed Power set Preorder Binary relation Ultrafilter (set theory) Mathematics Convergence in measure Locally compact Topology (structure) Hausdorff space Mathematical structures Topology Filter (set theory) Filters in topology Finite intersection property Family of sets Upper set Category (mathematics) Category of topological spaces Exponential object Topological space Topological properties Indiscrete topology Point-set topology Almost everywhere convergence Neighborhood filter Prefilter dbr:Pseudotopologies dbr:Pseudotopological_space
Link from a Wikipage to an external page	http://dolecki.perso.math.cnrs.fr/18dolecki.pdf http://dolecki.perso.math.cnrs.fr/init_IX07.pdf
sameAs	Convergence space Convergence space
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Cite_journal dbt:Em dbt:Math dbt:Refbegin dbt:Refend dbt:Reflist dbt:See_also dbt:Sfn dbt:Short_description dbt:Areas_of_mathematics dbt:Schechter_Handbook_of_Analysis_and_Its_Foundations dbt:Topology dbt:Dolecki_Mynard_Convergence_Foundations_Of_Topology
has abstract	In mathematics, a convergence space, also called a generalized convergence, is a set together with a relation called a convergence that satisfies certain properties relating elements of X with the family of filters on X. Convergence spaces generalize the notions of convergence that are found in point-set topology, including metric convergence and uniform convergence. Every topological space gives rise to a canonical convergence but there are convergences, known as non-topological convergences, that do not arise from any topological space. Examples of convergences that are in general non-topological include convergence in measure and almost everywhere convergence. Many topological properties have generalizations to convergence spaces. Besides its ability to describe notions of convergence that topologies are unable to, the category of convergence spaces has an important categorical property that the category of topological spaces lacks. The category of topological spaces is not an exponential category (or equivalently, it is not Cartesian closed) although it is contained in the exponential category of , which is itself a subcategory of the (also exponential) category of convergence spaces. (en)
prov:wasDerivedFrom	wikipedia-en:Convergence_space?oldid=1087341221&ns=0
page length (characters) of wiki page	16356 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Convergence_space
is rdfs:seeAlso of	Filters in topology
is Link from a Wikipage to another Wikipage of	Ultrafilter (set theory) Convergence in measure Closed set Hausdorff space Filters in topology Cauchy space Pointwise convergence Convergence Category of topological spaces T1 space Generalized convergence Preconvergence Preconvergence space
is Wikipage redirect of	Generalized convergence Preconvergence Preconvergence space
is Wikipage disambiguates of	Convergence
is foaf:primaryTopic of	wikipedia-en:Convergence_space

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