A Helly type Theorem for Convex Sets

Abstract A ray in Euclidean n-dimensional space Rn is a set of the form {a + λb: λ≥ 0 } where a and b are fixed points in Rn and b≠0. The subject of this paper is a Helly type theorem for convex sets in Rn . If is a finite family of at least 2n convex sets in Rn and if the intersection of any 2n members of contains a ray then contains a ray.