Ends of surface geometries, revisited
type: Item
instance of: scholarly article
title: Ends of surface geometries, revisited
zbMATH Open document ID: 0845.51012
DOI: 10.1007/BF01265636
published in: Geometriae Dedicata
publication date: 1996-09-02T00:00:00Z
review text: Let \({\mathcal E} = ({\mathcal S}, {\mathcal L})\) denote a stable plane [cf. chapter 23 by \textit{Th. Grundhöfer} and the author in F. Buekenhout (ed.), Handbook of incidence geometry, 1255-1324 (1995; Zbl 0824.51011)] for the definition and generalizations of this concept. If the point set \({\mathcal S}\) is a surface and the lines from \({\mathcal L}\) are connected, then the author proves without the assumption of finite connectivity (which in addition had been made by \textit{H. Salzmann} [Pac. J. Math. 29, 397-402 (1969; Zbl 0181.23301)] to derive the same theorem) that \({\mathcal S}\) is either the open disk, or the compact surface of characteristic 1, or the Möbius strip. The corresponding line spaces are also described under the weakened assumptions. Crucial arguments are provided by the use of the Freudenthal compactification of \({\mathcal S}\) [cf. \textit{J. R. Isbell}, `Uniform spaces' (1964; Zbl 0124.15601)].
Mathematics Subject Classification ID: 51H10
Mathematics Subject Classification ID: 51H20
Mathematics Subject Classification ID: 57N05
zbMATH DE Number: 826778
zbMATH Keywords: Möbius strip
zbMATH Keywords: ends of surfaces
zbMATH Keywords: stable plane
zbMATH Keywords: Freudenthal compactification
author: Rainer Löwen
reviewed by: Horst Szambien
MaRDI profile type: Publication
cites work: Q5593095
cites work: Q3660524
cites work: Topologische Geometrien auf dem Möbiusband
cites work: Metric collineations and inverse problems
cites work: Vierdimensionale stabile Ebenen
cites work: Central collineations and the parallel axiom in stable planes
cites work: Q5534009
cites work: Topologische Struktur zweidimensionaler projektiver Ebenen
cites work: Geometries on surfaces
full work available at URL: https://doi.org/10.1007/bf01265636
OpenAlex ID: W2073025093
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description: scientific article; zbMATH DE number 826778