Convex Set is Star Convex Set
Let $V$ be a vector space over $\R$ or $\C$.
Let $a \in A$.
Note that there is at least one point in $A$, as $A$ is non-empty.
If $x \in A$, then there is a line segment joining $a$ and $x$.
By definition of star convex set, it follows that $A$ is star convex, and $a$ is a star center.