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Compact spreads and compact translation planes over locally compact fields

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Abstract

We prove that a spread S over a locally compact nondlscrete field F defines a topological translation plane if and only if the spread is compact. For F=R, this is implicit in Breuning's thesis [Bre], cf. [B 2]. For the proof, we describe the point set of the projective translation plane as a quotient space of some projective space, with identifications taking place in one hyperplane. This is new even for F=R.

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  1. Abteilung für Topologie und Grundlagen der Analysis, Technische Universität Braunschweig, Pockelsstr. 14, D-3300, Braunschweig, W-Germany

    Rainer Löwen

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  1. Rainer Löwen
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Löwen, R. Compact spreads and compact translation planes over locally compact fields. J Geom 36, 110–116 (1989). https://doi.org/10.1007/BF01231026

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  • DOI: https://doi.org/10.1007/BF01231026

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