Divisible points of compact convex sets
type: Item
instance of: scholarly article
title: Divisible points of compact convex sets
zbMATH Open document ID: 0611.46011
DOI: 10.1007/BF02764963
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: A point in a compact convex set K in a real Hausdorff locally convex space is termed divisible if it occurs as the resultant (or barycentre) of each of a pair of mutually singular boundary probability measures. Roughly speaking, such points are the centres of mass of two disjointly supported weightings of the extreme points of K. The role which D(K) (the set of all divisible points of K) plays in determining the boundary probability measures associated with an arbitrary point is revealed. Also, the equivalence of D(K) with a set recently introduced by Reay for the particular case of convex polytopes is demonstrated. For polytopes, D(K) is a continuous image of a real projective space. A conjecture concerning D(K) is settled affirmatively for finite dimensional cubes.
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 46A50
Mathematics Subject Classification ID: 52Bxx
Mathematics Subject Classification ID: 52A05
zbMATH DE Number: 3987957
zbMATH Keywords: divisible points
zbMATH Keywords: compact convex sets
zbMATH Keywords: barycentre
zbMATH Keywords: convex polytopes
zbMATH Keywords: continuous image of a real projective space
author: Graham R. Wood
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02764963
OpenAlex ID: W1977895016
description: scientific article; zbMATH DE number 3987957