Definition:Separating Family of Seminorms on Vector Space

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

Let $X$ be a vector space over $\GF$.

Let $\PP$ be a set of seminorms on $X$.

We say that $\PP$ is separating for each $x \ne \mathbf 0_X$ we have $\map p x \ne 0$.