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 theintersection of any 2n members of contains a ray then containsa ray.

A form P of degree r is a homogeneous polynomial in k[Yi, …, Yn] on kn, k a field; Yi are the coordinate functions on kn. Let V(n, r) denote the k-vector space of forms of degree r. Mn(k) = Endk(kn) has canonical Lie algebra structure with [A, B] = AB-BA and it acts as a k-Lie Algebra of kderivations of degree 0 on k[Yi, …, Yn] defined by setting D(A)Y= Yo(-A) for A∈Endk(kn), Y∈V(n,l) = Homk(kn, k) and extending as a k-derivation. Define the orthogonal Lie Algebra, LO(P), of P by LO(P) =