Definition:Locally Compact Topological Vector Space

Definition

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

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

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

Sources

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