User:Caliburn/s/fa/Normed Vector Space with Separable Dual is Separable

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

Let $\struct {X^\ast, \norm \cdot_{X^\ast} }$ be the normed dual space of $X$.

Then, if $X^\ast$ is separable:


 * $X$ is separable.