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:


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

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