Definition:Bounded Subset of Normed Vector Space

Definition
Let $M = \struct {X, \norm {\, \cdot \,}}$ be a normed vector space.

Let $M' \subseteq X$.

Also see

 * Equivalence of Definitions of Bounded Subset of Normed Vector Space
 * Characterization of von Neumann-Boundedness in Normed Vector Space shows that this notion is equivalent to von Neumann-boundedness