# Definition:Star Convex Set/Star Center

## Definition

Let $V$ be a vector space over $\R$ or $\C$.

Suppose $A \subseteq V$ is a star convex set, so there exists $a \in A$ such that:

$\forall x \in A: \forall t \in \left[{0 \,.\,.\, 1}\right]: t x + \left({1 - t}\right) a \in A$

The point $a \in A$ is called a star center of $A$.