Definition:Hausdorff Topological Vector Space/Definition 2

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 :
 * for each $x \in X$, the singleton $\set x$ is closed in $\struct {X, \tau}$.