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Statements

Subject Item
dbr:Category_of_topological_vector_spaces
rdf:type
yago:Attribute100024264 yago:Space100028651 yago:Group100031264 dbo:TelevisionStation yago:Class107997703 yago:WikicatCategory-theoreticCategories yago:Collection107951464 yago:Abstraction100002137 yago:WikicatTopologicalVectorSpaces
rdfs:label
Category of topological vector spaces 位相線型空間の圏
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. 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。
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dbc:Categories_in_category_theory dbc:Topological_vector_spaces
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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。 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.
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