Definition:Hausdorff Topological Vector Space/Definition 1
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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.
Sources
Weisstein, Eric W. "Topological Vector Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TopologicalVectorSpace.html