Category:Von Neumann-Bounded Subsets of Topological Vector Spaces

This category contains results about Von Neumann-Bounded Subsets of Topological Vector Spaces.
Definitions specific to this category can be found in Definitions/Von Neumann-Bounded Subsets of Topological Vector Spaces.

Let $\Bbb F \in \set {\R, \C}$.

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

Let $E \subseteq X$.

We say that $E$ is von Neumann-bounded if and only if:

for each open neighbourhood $V$ of ${\mathbf 0}_X$, there exists $s > 0$ such that $E \subseteq t V$ for each $t > s$

where $t V$ is the dilation of $V$ by $t$.