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Transformations preserving adjacency and base subsets of spine spaces

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Abstract

Transformations of spine spaces which preserve base subsets preserve also adjacency. They either preserve the two sorts of projective adjacency or interchange them. Lines of a spine space can be defined in terms of adjacency, except one case where projective lines have no proper extensions to projective maximal strong subspaces, and thus adjacency preserving transformations are collineations.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Science of Ukraine, Tereshchenkivska 3, 01601, Kiev, Ukraine

    M. Pankov

  2. Institute of Mathematics, University of Bialystok, Akademicka 2, 15-267, Bialystok, Poland

    K. Prażmowski & M. Żynel

Authors
  1. M. Pankov
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  2. K. Prażmowski
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  3. M. Żynel
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Corresponding authors

Correspondence to M. Pankov, K. Prażmowski or M. Żynel.

Additional information

A. Kreuzer

The paper has been partly written during first author’s visit in the University of Bialystok.

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Pankov, M., Prażmowski, K. & Żynel, M. Transformations preserving adjacency and base subsets of spine spaces. Abh.Math.Semin.Univ.Hambg. 75, 21–50 (2005). https://doi.org/10.1007/BF02942034

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