Definition:Star Convex Set
Jump to navigation
Jump to search
Definition
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
- Star Shaped Set, which is a different definition.
Sources
- 2000: James R. Munkres: Topology (2nd ed.): $9$: The Fundamental Group: $\S 52$: The Fundamental Group
- 2001: Christian Berg: Kompleks funktionsteori: $\S 3.1$