Definition:Heine-Borel Property of Topological Vector Space

Definition

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

We say that $\struct {X, \tau}$ has the Heine-Borel property if and only if:

every closed von Neumann-bounded subset of $X$ is compact.

Sources

• 1991: Walter Rudin: Functional Analysis (2nd ed.) ... (previous) ... (next): $1.22$: Types of topological vector spaces