, Volume 24, Issue 1, pp 59–73 | Cite as

A Half-Space Approach to Order Dimension



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.


Convexity Quasiorder Preorder Half-space Dimension 

Mathematics Subject Classifications (2000)

06A06 06A07 52A01 


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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Institute of MathematicsTampere University of TechnologyTampereFinland
  2. 2.Institute of MathematicsUniversity of MiskolcMiskolcHungary

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