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 $\PP$ 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.