A

subset X of

**R**^{n} (or any

vector space over a

field of

characteristic 0) is called

*star convex* iff it contains some

point a∈X such that for any x∈X the entire

segment [a,x] = {tx+(1-t)a : 0<=t<=1} is contained in X.

That is, there's a point from which you can "see" all of the set.

Star convex sets needn't be convex (think of a 5-pointed star!), but any convex set is star convex (indeed, you can take a to be *any* point in the set).