Definition:Star Shaped Set

Definition
Let $V$ be a vector space over a field $K$.

Let $W \subseteq V$ be a subset of $V$.

Then $W$ is called a star shaped set iff for all $x \in W$, also $-x \in W$.

Here $-x$ is the inverse for $x$ with respect to vector addition in $V$.

Also known as
Sometimes one occurs the hyphenated form, i.e. star-shaped set.

A star shaped set is also known as a balanced set.