Definition:Normable Topological Vector Space

Definition

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

Let $\struct {X, \tau}$ be a topological vector space over $\GF$.

We say that $\struct {X, \tau}$ is normable if and only if:

there exists a norm $\norm {\, \cdot \,}$ on $X$ that induces $\tau$.

Sources

• 1991: Walter Rudin: Functional Analysis (2nd ed.) ... (previous) ... (next): $1.8$: Types of topological vector spaces