Definition:Star Shaped Set

Definition
Let $\mathcal{X}$ be a vector space over a field $K$, and $W\subseteq \mathcal{X}$.

$W$ is called star shaped if whenever $x\in W$ then $-x\in W$.

Note : We should clarify the meaning of the element $-x$ in the definition. The algebraic structure $(\mathcal{X},+)$ is an abelian group, therefore for each $x\in\mathcal{X}$ there is a $-x\in\mathcal{X}$ such that $x+(-x)=0_\mathcal{X}$ where $0_\mathcal{X}$ is the zero vector of $\mathcal{X}$.

Other Names
A star-shaped set is also known as balanced.