Definition:Locally Bounded Topological Vector Space
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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