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 continuous. The category is often denoted TVect or TVS.

Fixing a topological field K, one can also consider the (sub-)category TVectK of topological vector spaces over K with continuous K-linear maps as the morphisms.

Read more about Category Of Topological Vector SpacesTVect Is A Concrete Category, Is A Topological Category

Other articles related to "category of topological vector spaces, category, topological, category of, spaces, vector space, vector spaces, topological vector space":

Category Of Topological Vector Spaces - Is A Topological Category
... The category is topological, which means loosely speaken that it relates to its "underlying category" the category of vector spaces in the same way that Top relates to Set ... Formally For every single K-vector space and every family of topological K-vector spaces and K-linear maps, there exists a vector space topology on so that the following property is fulfilled Whenever is a K-linear ... The topological vector space is called "initial object" or "initial structure" with respect to the given data ...

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