nLab
star-shaped neighborhood

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

More generally, for XX a real affine space, star shaped neighbourhood of a point xXx\in X is an open neighbourhood UXU \subset X such that with yXy \in X, the straight line segment connecting xx with yy in XX is also contained in UU.

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