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Continuous Representations of Interval Orders by Means of Two Continuous Functions

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Listed:
  • Gianni Bosi

    (University of Trieste)

  • Asier Estevan

    (Universidad Pública de Navarra. Institute INAMAT)

Abstract

In this paper, we provide a characterization of the existence of a representation of an interval order on a topological space in the general case by means of a pair of continuous functions, when neither the functions nor the topological space are required to satisfy any particular assumptions. Such a characterization is based on a suitable continuity assumption of the binary relation, called weak continuity. In this way, we generalize all the previous results on the continuous representability of interval orders, and also of total preorders, as particular cases.

Suggested Citation

  • Gianni Bosi & Asier Estevan, 2020. "Continuous Representations of Interval Orders by Means of Two Continuous Functions," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 700-710, June.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:3:d:10.1007_s10957-020-01675-0
    DOI: 10.1007/s10957-020-01675-0
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    References listed on IDEAS

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    1. Chateauneuf, Alain, 1987. "Continuous representation of a preference relation on a connected topological space," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 139-146, April.
    2. Bridges, Douglas S., 1986. "Numerical representation of interval orders on a topological space," Journal of Economic Theory, Elsevier, vol. 38(1), pages 160-166, February.
    3. Herden, Gerhard & Pallack, Andreas, 2002. "On the continuous analogue of the Szpilrajn Theorem I," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 115-134, March.
    4. Oloriz, Esteban & Candeal, Juan Carlos & Indurain, Esteban, 1998. "Representability of Interval Orders," Journal of Economic Theory, Elsevier, vol. 78(1), pages 219-227, January.
    5. Bosi, Gianni & Zuanon, Magalì, 2011. "Weak continuity of preferences with nontransitive indifference," MPRA Paper 34182, University Library of Munich, Germany.
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