Abstract
The concept of an ordered projective Hjelmslev plane was intuitively introduced by Hjelmslev in “Einleitung in die allgemeine Kongruenglehre” ([9], [10]).
This paper is concerned with formalizing and examing preorderings and orderings for projective Hjelmslev planes. In addition we show that orderings generated topologies of the point and line sets which render the plane a topological Hjelmslev plane ([19], [13]). These planes — unlike the ordinary ordered planes ([18]) — are, due to the existence of infinitesimals, non-archimedian, non-compact and disconnected with the neighbour classes as certain quasi-components.
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The authors gratefully acknowledge the support of the Natural Sciences and Engineering Research Council of Canada.
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Baker, C., Lane, N.D. & Lorimer, J.W. Order and topology in projective Hjelmslev planes. J Geom 19, 8–42 (1982). https://doi.org/10.1007/BF01930867
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DOI: https://doi.org/10.1007/BF01930867