Existence conditions for dualities of projective planes
type: Item
instance of: scholarly article
title: Existence conditions for dualities of projective planes
zbMATH Open document ID: 1006.51001
published in: Archiv der Mathematik
publication date: 2002-05-21T00:00:00Z
review text: The author investigates projective planes satisfying specific incidence axioms which are particular cases of the theorems of Desargues and Pappos, respectively. Examples are provided by planes which are coordinatized by commutative quasifields. The main result of the paper shows that the planes in question admit a naturally defined duality. If the plane is topological, then the existence of a duality implies that the point space is homeomorphic to the line space, thanks to a result of \textit{R. Bödi} and \textit{L. Kramer} [Geom. Dedicata 58, No. 1, 1-14 (1995; Zbl 0836.51001)].
Mathematics Subject Classification ID: 51A10
Mathematics Subject Classification ID: 51H10
zbMATH DE Number: 1742831
zbMATH Keywords: projective planes
zbMATH Keywords: dualities
zbMATH Keywords: topological projective planes
author: Guenter Pickert
reviewed by: Harald Löwe
MaRDI profile type: Publication
full work available at URL: s00013-002-8229-x
OpenAlex ID: W2316715437
DOI: 10.1007/S00013-002-8229-X
description: scientific article; zbMATH DE number 1742831