Star-shaped space

In mathematics, a set $S$ in the Euclidean space ${\mathbb{R}}^n$ is called a star domain (or star-convex set, star-shaped set or radially convex set) if there exists an $s_0\in S$ such that for all $s\in S$ the line segment from $s_0$ to $s$ lies in $S$. This definition is immediately generalizable to any real or complex vector space.

Star-shaped implies contractible space.