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A Half-Space Approach to Order Dimension

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Abstract

The aim of the present paper is to investigate the half-spaces in the convexity structure of all quasiorders on a given set and to use them in an alternative approach to classical order dimension. The main result states that linear orders can almost always be replaced by half-space quasiorders in the definition of the dimension of a partially ordered set.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Tampere University of Technology, PL 553, Tampere, 33101, Finland

    Stephan Foldes

  2. Institute of Mathematics, University of Miskolc, Miskolc-Egyetemvaros, Miskolc, 3515, Hungary

    Jenő Szigeti

Authors
  1. Stephan Foldes
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  2. Jenő Szigeti
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Corresponding author

Correspondence to Jenő Szigeti.

Additional information

The work of the first named author was partially supported by the European Community’s Marie Curie Program (contract MTKD-CT-2004-003006). The second named author’s work was supported by OTKA of Hungary No. T043034.

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Foldes, S., Szigeti, J. A Half-Space Approach to Order Dimension. Order 24, 59–73 (2007). https://doi.org/10.1007/s11083-007-9059-z

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  • DOI: https://doi.org/10.1007/s11083-007-9059-z

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