Zur Fortsetzbarkeit von Ordnungsfunktionen einer affinen Ebene. (Extension of order functions of affine planes)
type: Item
instance of: scholarly article
title: Zur Fortsetzbarkeit von Ordnungsfunktionen einer affinen Ebene. (Extension of order functions of affine planes)
zbMATH Open document ID: 0598.51002
DOI: 10.1007/BF01227841
author: Hans-Joachim Kroll
published in: Journal of Geometry
publication date: 1986-01-01T00:00:00Z
review text: An order function of a plane associates a number 1 or -1 with every triple consisting of a line and a pair of points not on the line, and is required to satisfy two conditions. Such an order function is an extension of the idea of two points lying on the same side or on opposite sides of a line. Let \(\Delta_ y\) denote the group of dilatations of an affine plane with centre y. The author shows that if for a point y of an affine translation plane \(| \Delta_ y| \geq 3\), then every order function of the plane can be extended to the projective closure.
Mathematics Subject Classification ID: 51A35
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51G05
zbMATH DE Number: 3964843
zbMATH Keywords: order function
zbMATH Keywords: affine translation plane
MaRDI profile type: Publication
cites work: Q5565568
cites work: Über die projektive Erweiterungsfähigkeit affiner Ordnungsfunktionen
cites work: Zur Fortsetzung affiner Ordnungsfunktionen
cites work: Die Ordnungsfunktionen einer Geometrie
cites work: Q5794097
cites work: Konvexität bei Ordnungsfunktionen
description: scientific article; zbMATH DE number 3964843