Theorems on the existence of separating surfaces
type: Item
instance of: scholarly article
title: Theorems on the existence of separating surfaces
zbMATH Open document ID: 0723.52002
DOI: 10.1007/BF02574673
author: Michael E. Houle
published in: Discrete \& Computational Geometry
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/131142
review text: Let R and G be finite sets in \(E^ d\). Kirchberger's theorem implies that the strict linear separability of R and G is determined by the separability of all subsets of up to \(d+2\) points of \(R\cup G\). This paper shows that under certain conditions, the linear separability of R and G is determined by the separability of significantly fewer than all subfamilies of up to \(d+2\) members of R and G. The same treatment is made of Lay's extension of Kirchberger's theorem to separation by hyperspheres.
Mathematics Subject Classification ID: 52A35
zbMATH DE Number: 4192532
zbMATH Keywords: Helly's theorem
zbMATH Keywords: separation of finite sets
zbMATH Keywords: Kirchberger's theorem
MaRDI profile type: Publication
cites work: Q5341481
cites work: Q5633198
cites work: Q3644247
cites work: On Separation by Spherical Surfaces
cites work: Helly's Theorems on Convex Domains and Tchebycheff's Approximation Problem
cites work: A refinement of theorems of Kirchberger and Carathéodory
description: scientific article; zbMATH DE number 4192532