Definition:Locally Convex Space

Definition
Let $\Bbb F \in \set {\R, \C}$.

Let $X$ be a vector space over $\Bbb F$.

Let $\mathcal P$ be a set of seminorms on $X$.

We call the pair $\struct {X, \mathcal P}$ a locally convex space.

Also see

 * Characterization of Topological Vector Spaces Isomorphic to Locally Convex Space