Definition:Star Convex Set

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

A subset $A \subseteq V$ is said to be star convex iff 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 $A$.

A star convex set can thus be described as a set containing all line segments between the star center and an element of the set.

Also known as
A star convex set is also called a star domain, a star-like set, a star-shaped set, or a radially convex set.

The hyphenated form star-convex set is also used.

Also see

 * Star Shaped Set, which is a different definition.