# nLab star-shaped neighborhood

For $V$ a vector space, a star shaped neighbourhood of the origin is an open neighbourhood $U \subset V$ such that with $v \in U$ and $s \in [0,1]$ also $s v \in U$.

More generally, for $X$ a real affine space, star shaped neighbourhood of a point $x\in X$ is an open neighbourhood $U \subset X$ such that with $y \in X$, the straight line segment connecting $x$ with $y$ in $X$ is also contained in $U$.

Revised on August 27, 2013 07:34:27 by Colin Tan (183.90.103.178)