\begin{definition}[Definition:Separable Space/Normed Vector Space]
Let $M = \struct {X, \norm {\, \cdot \,} }$ be a normed vector space.
Let $Y \subseteq X$ be a subset of $X$.
Let $Y$ be (everywhere) dense in $X$.
Let $Y$ be a countable set:
:$Y = \set {y_1, y_2, \ldots}$
Suppose:
:$\forall x \in X : \forall \epsilon \in \R : \epsilon > 0 : \exists y_{n \mathop \in \N} \in Y : \norm {y_n - x} < \epsilon$
Then $X$ is '''separable'''.
\end{definition}