An extension of Radon's theorem

Abstract

introduction Let "m-set" mean a set of m points in the d-dimensional space R . An m-set is said to be (r, )-divisible if it can be partitioned into r pair-wise dis- joint subsets in such a way that the intersection of the convex hulls of these r subsets is at least It-dimensional. (We always assume 0 _ / _ d. The empty set is (-1)-dimensional, while 0-dimensional sets are non-empty.) A classic theorem of J. Radon The first generalization for r > 2 was given by R. Rado