Definition:Hausdorff Topological Vector Space/Definition 1

Definition

Let $K$ be a topological field.

Let $\struct {X, \tau}$ be a topological vector space over $K$.

We say that $\struct {X, \tau}$ is a Hausdorff topological vector space if and only if it is Hausdorff as a topological space.

Also see

• Equivalence of Definitions of Hausdorff Topological Vector Space

• Results about Hausdorff topological vector spaces can be found here.

Sources

• Weisstein, Eric W. "Topological Vector Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TopologicalVectorSpace.html