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Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions

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  • Bosi, Gianni
  • Caterino, Alessandro
  • Ceppitelli, Rita

Abstract

We present new sufficient conditions for the existence of a continuous utility function for an arbitrary binary relation on a topological space. Such conditions are basically obtained by using both the concept of a weakly continuous binary relation on a topological space and the concept of a countable network weight. In particular, we are concerned with suitable topological notions which generalize the concept of compactness and do not imply second countability or local compactness.

Suggested Citation

  • Bosi, Gianni & Caterino, Alessandro & Ceppitelli, Rita, 2009. "Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions," MPRA Paper 14808, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:14808
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    File URL: https://mpra.ub.uni-muenchen.de/14808/1/MPRA_paper_14808.pdf
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    References listed on IDEAS

    as
    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. Back, Kerry, 1986. "Concepts of similarity for utility functions," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 129-142, April.
    3. Bosi, G. & Mehta, G. B., 2002. "Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 311-328, November.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Alcantud, José Carlos R. & Bosi, Gianni & Zuanon, Magalì, 2013. "Representations of preorders by strong multi-objective functions," MPRA Paper 52329, University Library of Munich, Germany.
    2. José Carlos R. Alcantud & Gianni Bosi & Magalì Zuanon, 2016. "Richter–Peleg multi-utility representations of preorders," Theory and Decision, Springer, vol. 80(3), pages 443-450, March.

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    More about this item

    Keywords

    hereditarily Lindeloef space; weakly continuous binary relation; countable network weight; hemicompactness; submetrizability;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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