# 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:

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

### Star Center

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.