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 if and only if:

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

Sources

• 1991: Walter Rudin: Functional Analysis (2nd ed.) ... (previous) ... (next): $1.6$: Topological vector spaces