Definition:Everywhere Dense/Normed Vector Space

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

Let $Y \subseteq X$ be a subset of $X$.

Suppose:


 * $\forall x \in X: \forall \epsilon \in \R_{>0}: \exists y \in Y: \norm {x - y} < \epsilon$

Then $Y$ is (everywhere) dense in $X$.