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On continuous multi-utility representations of semi-closed and closed preorders

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  • Bosi, Gianni
  • Herden, Gerhard

Abstract

On the basis of the classical continuous multi-utility representation theorem of Levin on locally compact and σ-compact Hausdorff spaces, we present necessary and sufficient conditions on a topological space (X,t) under which every semi-closed and closed preorder respectively admits a continuous multi-utility representation. This discussion provides the fundaments of a mainly topological theory that systematically combines topological and order theoretic aspects of the continuous multi-utility representation problem.

Suggested Citation

  • Bosi, Gianni & Herden, Gerhard, 2016. "On continuous multi-utility representations of semi-closed and closed preorders," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 20-29.
    • Handle: RePEc:eee:matsoc:v:79:y:2016:i:c:p:20-29
    DOI: 10.1016/j.mathsocsci.2015.10.006
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    References listed on IDEAS

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    5. Pivato, Marcus, 2013. "Multiutility representations for incomplete difference preorders," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 196-220.
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    Cited by:

    1. Knoblauch, Vicki, 2016. "Elections generate all binary relations on infinite sets," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 105-108.
    2. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2021. "Expected utility theory on mixture spaces without the completeness axiom," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    3. Gianni Bosi & Laura Franzoi, 2023. "A simple characterization of the existence of upper semicontinuous order-preserving functions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 203-210, October.
    4. Gianni Bosi & Asier Estevan & Armajac Raventós-Pujol, 2020. "Topologies for semicontinuous Richter–Peleg multi-utilities," Theory and Decision, Springer, vol. 88(3), pages 457-470, April.
    5. Pedro Hack & Daniel A. Braun & Sebastian Gottwald, 2023. "The classification of preordered spaces in terms of monotones: complexity and optimization," Theory and Decision, Springer, vol. 94(4), pages 693-720, May.

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