Archiv der Mathematik

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

Lexicographic behaviour of chains

  • Juan C. Candeal
  • Esteban Induráin


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.


Utility Function Numerical Representation Planar Chain Lexicographic Product Connected Chain 
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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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