About: Coherent topology

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In topology, a coherent topology is a topology that is uniquely determined by a family of subspaces. Loosely speaking, a topological space is coherent with a family of subspaces if it is a topological union of those subspaces. It is also sometimes called the weak topology generated by the family of subspaces, a notion that is quite different from the notion of a weak topology generated by a set of maps.

Attributes	Values
rdfs:label	Coherent topology (en) Topologie cohérente (fr)
rdfs:comment	In topology, a coherent topology is a topology that is uniquely determined by a family of subspaces. Loosely speaking, a topological space is coherent with a family of subspaces if it is a topological union of those subspaces. It is also sometimes called the weak topology generated by the family of subspaces, a notion that is quite different from the notion of a weak topology generated by a set of maps. (en) La topologie cohérente est fréquemment utilisée en topologie algébrique, notamment en lien avec les limites inductives. Ce vocable désigne à la fois une méthode assez générale pour construire une topologie mais aussi une topologie particulière des espaces vectoriels réels de dimension infinie. (fr)
dcterms:subject	General topology
Wikipage page ID	14602178 (xsd:integer)
Wikipage revision ID	1081473108 (xsd:integer)
Link from a Wikipage to another Wikipage	Topological embedding Homeomorphic Inclusion map Compact space Closed map Limit (category theory) Closed set Compactly generated space Comparison of topologies Empty set Topology Weak topology Disjoint union (topology) Locally finite collection Equivalence relation Direct limit Directed set Finitely generated space Quotient space (topology) Refinement (topology) Intersection (set theory) Cover (topology) General topology Discrete space CW complex Final topology Continuous function (topology) Indexed family Induced topology Open cover Open map Open set Category of topological spaces Subspace topology Finite topological space Universal property Topological space Set-theoretic union Finest topology Disjoint set Quotient map Partition (set theory) Subspace (topology) Surjective map
Link from a Wikipage to an external page	https://archive.org/details/generaltopology00will_0%7Curl-access=registration%7Cpublisher=Addison-Wesley%7Clocation=Reading,
sameAs	Coherent topology Coherent topology Coherent topology Coherent topology Coherent topology
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Cite_book dbt:Cite_encyclopedia dbt:Reflist dbt:Short_description
has abstract	In topology, a coherent topology is a topology that is uniquely determined by a family of subspaces. Loosely speaking, a topological space is coherent with a family of subspaces if it is a topological union of those subspaces. It is also sometimes called the weak topology generated by the family of subspaces, a notion that is quite different from the notion of a weak topology generated by a set of maps. (en) La topologie cohérente est fréquemment utilisée en topologie algébrique, notamment en lien avec les limites inductives. Ce vocable désigne à la fois une méthode assez générale pour construire une topologie mais aussi une topologie particulière des espaces vectoriels réels de dimension infinie. (fr)
gold:hypernym	Topology
prov:wasDerivedFrom	wikipedia-en:Coherent_topology?oldid=1081473108&ns=0
page length (characters) of wiki page	8992 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Coherent_topology
is Link from a Wikipage to another Wikipage of	Topological union Topology determined by a cover Alexandrov topology Compactly generated space Final topology Sequence space Union (topology)
is Wikipage redirect of	Topological union Topology determined by a cover Union (topology)
is foaf:primaryTopic of	wikipedia-en:Coherent_topology

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