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 $x_0$ in $S$ such that for all $x$ in $S$ the line segment from $x_0$ to $x$ is in $S$
What are the requirements on the line segment? it must be a straight line? right? if no, so every simple-connected set will be a star domain which is incorrect
Yes, the phrase "line segment" means a straight line.