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On the existence of topological ovals in flat projective planes

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Abstract

We show that every flat projective plane contains topological ovals. This is achieved by completing certain closed partial ovals, the so-called quasi-ovals, to topological ovals.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Adelaide, 5005, Adelaide, S. A., Australia

    B. Polster

  2. Mathematisches Seminar, Universität Kiel, Ludewig-Meyn-Straße 4, D-24098, Kiel

    N. Rosehr

  3. Department of Mathematics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

    G. F. Steinke

Authors
  1. B. Polster
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  2. N. Rosehr
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  3. G. F. Steinke
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Additional information

This research was supported for the first and second author by a Feodor Lynen Fellowship and by a DAAD scholarship, respectively.

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Polster, B., Rosehr, N. & Steinke, G.F. On the existence of topological ovals in flat projective planes. Arch. Math. 68, 418–429 (1997). https://doi.org/10.1007/s000130050074

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  • DOI: https://doi.org/10.1007/s000130050074

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