Partial affine spaces of dimension \(\geq 3\)
type: Item
instance of: scholarly article
title: Partial affine spaces of dimension \(\geq 3\)
zbMATH Open document ID: 0854.51002
DOI: 10.1007/BF01222688
author: Stephan Meuren
published in: Journal of Geometry
publication date: 1997-01-19T00:00:00Z
review text: An incidence structure \((P, {\mathcal G})\) is called a partial linear space if two points are on at most one line and, dually, two lines have at most one point in common. A partial linear space with parallelism is called a partial affine space if there exists an affine space \((P,{\mathcal G}')\) such that \({\mathcal G} \subseteq {\mathcal G}'\) and such that the parallel relation on \(\mathcal G\) is induced from the natural parallelism in \({\mathcal G}'\). Let \((P,{\mathcal G})\) be a partial linear space with parallelism such that the Tamaschke configuration is closed. If certain conditions are fulfilled, which make sure that there are ``enough'' connectible points in \(P\), and that the dimension is at least three, then \((P,{\mathcal G})\) is a partial affine space. The theorem has been proved by \textit{A. Herzer} and the author [J. Geom. 50, No. 1-2, 124-142 (1994; Zbl 0807.51002)], and improved by \textit{V. Pambuccian} [J. Geom 55, No. 1-2, 139-140 (1996)], under the assumption that the dimension is at least four.
reviewed by: Hubert Kiechle
Mathematics Subject Classification ID: 51A15
Mathematics Subject Classification ID: 51A20
Mathematics Subject Classification ID: 51A45
zbMATH DE Number: 913040
zbMATH Keywords: embeddable into affine space
zbMATH Keywords: partial affine space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 913040