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Archiv der Mathematik

, Volume 72, Issue 2, pp 145–152 | Cite as

Lexicographic behaviour of chains

  • Juan C. Candeal
  • Esteban Induráin

Abstract.

This paper introduces a different approach to the study of the existence of numerical representations of totally ordered sets (chains). We pay attention to the properties of non-representable chains showing that, under certain conditions, those chains must have a sort of lexicographic behaviour similar to that of the lexicographic plane. We prove that a countably bounded connected chain \((Z, \prec )\) admits a lexicographic decomposition as a subset of the lexicographic product \(\Bbb R \times Z\). Then we apply our approach to state both a sufficient and a necessary condition for the lack of utility functions. The concept of planar chain is also introduced.

Keywords

Utility Function Numerical Representation Planar Chain Lexicographic Product Connected Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • Juan C. Candeal
    • 1
  • Esteban Induráin
    • 2
  1. 1.Universidad de Zaragoza, Facultad de Ciencias Económicas y Empresariales, Departamento de Análisis Económico, c/ Doctor Cerrada 1 – 3, E-50005-Zaragoza, SpainES
  2. 2.Universidad Pública de Navarra, Departamento de Matemática e Informática, Campus Arrosadía s.n, E-31006-Pamplona, SpainES

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