Definition:Star Convex Set

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

A subset $A \subseteq V$ is said to be star convex if and only if 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

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