Vol. 59, No. 2, 1975

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Radon partitions in real linear spaces

Clinton M. Petty

Vol. 59 (1975), No. 2, 515–523
Abstract

An intimate connection is established between primitive Radon partitions and generalized poonems of a set in a real linear space . 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
Authors
Clinton M. Petty