Definition:Locally Bounded Topological Vector Space

Definition

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

We say that $X$ is locally bounded if and only if:

there exists a von Neumann-bounded open neighborhood of ${\mathbf 0}_X$.

Sources

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