starshaped region
Definition A subset $U$ of a real (or possibly complex) vector space^{} is called starshaped if there is a point $p\in U$ such that the line segment^{} $\overline{pq}$ is contained in $U$ for all $q\in U$. (Here, $\overline{pq}=\{tp+(1t)qt\in [0,1]\}$.) We then say that $U$ is starshaped with respect to $p$.
In other , a region $U$ is starshaped if there is a point $p\in U$ such that $U$ can be “collapsed” or “contracted” $p$.
0.0.1 Examples

1.
In ${\mathbb{R}}^{n}$, any vector subspace is starshaped. Also, the unit cube and unit ball^{} are starshaped, but the unit sphere^{} is not.

2.
A subset $U$ of a vector space is starshaped with respect to all of its points if and only if $U$ is convex.
Title  starshaped region 

Canonical name  StarshapedRegion 
Date of creation  20130322 13:34:13 
Last modified on  20130322 13:34:13 
Owner  matte (1858) 
Last modified by  matte (1858) 
Numerical id  10 
Author  matte (1858) 
Entry type  Definition 
Classification  msc 52A30 
Classification  msc 32F99 
Defines  starshaped 