Definition:Bounded Subset of Normed Vector Space/Definition 2
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Definition
Let $M = \struct {X, \norm {\, \cdot \,}}$ be a normed vector space.
Let $M' = \struct {Y, \norm {\, \cdot \,}_Y}$ be a subspace of $M$.
$M'$ is bounded (in $M$) if and only if:
- $\exists \epsilon \in \R_{>0} : \exists x \in X : Y \subseteq \map {B_\epsilon^-} x$
where $\map {B_\epsilon^-} x$ is a closed ball in $M$.