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 **TVect**_{K} 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

### 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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