Definition:Von Neumann-Bounded Subset of Topological Vector Space

Definition
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 :


 * 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 $t$.

Also see

 * Definition:Bounded Subset of Topological Vector Space