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Linear geometries on the Moebius strip: A theorem of Skornyakov type

Published online by Cambridge University Press:  17 April 2009

Rainer Löwen  and
Burkard Polster
Rainer Löwen
Affiliation:
Institut für Analysis und Algebra, Technische Universität, Pockelsstr. 14, 38106 Braunschweig, Germany, e-mail: r.loewen@tu-bs.de
Burkard Polster
Affiliation:
School of Mathematical Sciences, Monash University, Victoria 3800, Australia, e-mail: Burkard.Polster@sci.monash.edu.au
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We show that the continuity properties of a stable plane are automatically satisfied if we have a linear space with point set a Moebius strip, provided that the lines are closed subsets homeomorphic to the real line or to the circle. In other words, existence of a unique line joining two distinct points implies continuity of join and intersection. For linear spaces with an open disk as point set, the same result was proved by Skornyakov.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 1 , August 2005 , pp. 17 - 30
Copyright
Copyright © Australian Mathematical Society 2005

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