---- > [!definition] Definition. ([[topological vector space]]) > A **topological vector space (TVS)** is a [[topological space]] that is also a [[vector space]] such that addition and scalar multiplication are [[continuous]]. > The [[category]] of [[topological vector space|topological vector spaces]] and [[linear map|linear]] [[continuous]] maps between them (so-called **toplinear maps**) is denoted $\mathsf{TVS}$. ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```