Definition:Locally Convex Space/Hausdorff

Definition

Let $\struct {X, \mathcal P}$ be a locally convex space.

We say that $\struct {X, \mathcal P}$ is Hausdorff if and only if $\PP$ is separating.

Also see

• Locally Convex Space is Hausdorff iff induces Hausdorff Topology justifies the use of the term "Hausdorff" by showing that the standard topology on a Hausdorff locally convex space is Hausdorff. Conversely, if the standard topology of a locally convex space is Hausdorff, then the space is Hausdorff as a locally convex space.

Sources

• 2011: Graham R. Allan and H. Garth Dales: Introduction to Banach Spaces and Algebras ... (previous) ... (next): $3.3$: A note on locally convex spaces