Topological vector spaces | Categories in category theory

Category of topological vector spaces

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. (Wikipedia).

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Category of sets | Concrete category | Subcategory | Forgetful functor | Category of topological spaces | Vector space | Mathematics | Set (mathematics) | Function (mathematics) | Function composition | Topology | Topological vector space | Morphism