A
subset X of
Rn (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).