\begin{definition}[Definition:Bounded Normed Vector Space/Definition 2]
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 $M$)''' {{iff}}:
:$\exists \epsilon \in \R_{>0} : \exists x \in X : Y \subseteq \map {B_\epsilon^-} x$
where $\map {B_\epsilon^-} x$ is a closed ball in $M$.
\end{definition}