About: Category of topological vector spaces

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In mathematics, the category of topological vector spaces is the category whose objects are topological vector spaces and whose morphisms are continuous linear maps between them. This is a category because the composition of two continuous linear maps is again a continuous linear map. The category is often denoted TVect or TVS. Fixing a topological field K, one can also consider the subcategory TVectK of topological vector spaces over K with continuous K-linear maps as the morphisms.

Attributes	Values
rdf:type	yago:WikicatCategory-theoreticCategories yago:WikicatTopologicalVectorSpaces yago:Abstraction100002137 yago:Attribute100024264 yago:Class107997703 yago:Collection107951464 yago:Group100031264 television station yago:Space100028651
rdfs:label	Category of topological vector spaces (en) 位相線型空間の圏 (ja)
rdfs:comment	In mathematics, the category of topological vector spaces is the category whose objects are topological vector spaces and whose morphisms are continuous linear maps between them. This is a category because the composition of two continuous linear maps is again a continuous linear map. The category is often denoted TVect or TVS. Fixing a topological field K, one can also consider the subcategory TVectK of topological vector spaces over K with continuous K-linear maps as the morphisms. (en) 数学の一分野、圏論における位相線型空間の圏（いそうせんけいくうかんのけん、英: category of topological vector spaces）TVect（あるいは TVS などとも書く）は、すべての位相線型空間を対象とし、すべての連続線型写像を射とする圏である。これが圏を成すのは、二つの連続線型写像の合成がふたたび連続線型となることによる。位相体 K を一つ固定して、K 上の位相線型空間が連続 K-線型写像を射としてなす（部分）圏 TVectK を考えることもできる。 (ja)
dcterms:subject	Topological vector spaces Categories in category theory
Wikipage page ID	15089522 (xsd:integer)
Wikipage revision ID	1071179856 (xsd:integer)
Link from a Wikipage to another Wikipage	Subcategory Topological vector spaces Vector space Continuous linear map Mathematics Function (mathematics) Function composition Morphism Concrete category Category (category theory) Category of sets Topological field Topological vector space Topology Forgetful functor Categories in category theory Category of topological spaces Set (mathematics) Category of vector spaces Object (category theory)
sameAs	Category of topological vector spaces Category of topological vector spaces Category of topological vector spaces Category of topological vector spaces Category of topological vector spaces
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Cite_book dbt:Clarify dbt:Short_description
has abstract	In mathematics, the category of topological vector spaces is the category whose objects are topological vector spaces and whose morphisms are continuous linear maps between them. This is a category because the composition of two continuous linear maps is again a continuous linear map. The category is often denoted TVect or TVS. Fixing a topological field K, one can also consider the subcategory TVectK of topological vector spaces over K with continuous K-linear maps as the morphisms. (en) 数学の一分野、圏論における位相線型空間の圏（いそうせんけいくうかんのけん、英: category of topological vector spaces）TVect（あるいは TVS などとも書く）は、すべての位相線型空間を対象とし、すべての連続線型写像を射とする圏である。これが圏を成すのは、二つの連続線型写像の合成がふたたび連続線型となることによる。位相体 K を一つ固定して、K 上の位相線型空間が連続 K-線型写像を射としてなす（部分）圏 TVectK を考えることもできる。 (ja)
gold:hypernym	Category
prov:wasDerivedFrom	wikipedia-en:Category_of_topological_vector_spaces?oldid=1071179856&ns=0
page length (characters) of wiki page	4850 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Category_of_topological_vector_spaces
is Link from a Wikipage to another Wikipage of	Continuous embedding
is foaf:primaryTopic of	wikipedia-en:Category_of_topological_vector_spaces

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