Interval Orders

  • Douglas S. Bridges
  • Ghanshyam B. Mehta
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 422)


In this chapter we deal with interval orders and their representation by pairs of real-valued functions. The notion of an interval order is introduced in Section 1, where we also construct a representation when the underlying set is countable. In Section 2 we discuss various topological properties of an interval order on a topological space X. This prepares the way for the case where X is a topological space and we seek representing functions with appropriate continuity properties. Section 3 covers the case where X is a convex subset of N-dimensional euclidean space, when we extend the Arrow-Hahn approach described in Chapter 2. Section 4 contains some representation theorems applicable when X is a topological space. The final section describes Chateauneuf’s theorem, giving necessary and sufficient conditions for the existence of a pair of continuous functions representing an interval order on a topological space.


Topological Space Lower Semicontinuous Continuous Representation Interval Order Strict Partial Order 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Douglas S. Bridges
    • 1
  • Ghanshyam B. Mehta
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of WaikatoHamiltonNew Zealand
  2. 2.Department of EconomicsUniversity of QueenslandBrisbaneAustralia

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