Radon partitions in real linear spaces

Clinton M. Petty

Vol. 59 (1975), No. 2, 515–523

DOI: 10.2140/pjm.1975.59.515

Abstract

An intimate connection is established between primitive Radon partitions and generalized poonems of a set in a real linear space ℒ. It is shown that if K ⊂ℒ is convex then K is the convex hull of its extreme points if and only if the intersection of poonems of K is a poonem of K. Among the applications is a study of k-neighborly sets. This yields a considerable generalization of the theory of k-neighborly polytopes.

Mathematical Subject Classification 2000

Primary: 52A05

Milestones

Received: 24 May 1974

Revised: 12 June 1975

Published: 1 August 1975