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.
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Author of the notes: Antonio J. Pan-Collantes
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