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 Spaces: TVect Is A Concrete Category, Is A Topological Category
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