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 there exists $a \in A$ such that:


 * $\forall x \in A: \forall t \in \closedint 0 1: t x + \paren {1 - t} a \in A$

Star Center
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.