Separating hyperplanes for convex sets over ordered fields
type: Item
instance of: scholarly article
title: Separating hyperplanes for convex sets over ordered fields
zbMATH Open document ID: 0566.12011
DOI: 10.1216/RMJ-1984-14-4-991
author: Jonathan Lee Merzel
published in: Rocky Mountain Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Let \((F,<)\) be an ordered field. Theorem. If A,B are disjoint convex sets in \(F^ n\), then the ordering of F can be extended to an ordering of the rational function field \(K=F(t_ 1,...,t_ n)\) in such a way that A,B are strongly separated by a hyperplane in \(K^ n\).
Mathematics Subject Classification ID: 12D15
Mathematics Subject Classification ID: 12J15
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 3902782
zbMATH Keywords: separating hyperplanes
zbMATH Keywords: ordered field
zbMATH Keywords: convex sets
zbMATH Keywords: ordering of the rational function field
MaRDI profile type: Publication
full work available at URL: rmj-1984-14-4-991
OpenAlex ID: W2061926817
description: scientific article; zbMATH DE number 3902782