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New characterizations of completely useful topologies in mathematical utility theory

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  • Gianni Bosi
  • Roberto Daris
  • Gabriele Sbaiz

Abstract

Let $X$ be an arbitrary set. Then a topology $t$ on $X$ is said to be completely useful if every upper semicontinuous linear (total) preorder $\precsim$ on $X$ can be represented by an upper semicontinuous real-valued order preserving function. In this paper, appealing, simple and new characterizations of completely useful topologies will be proved, therefore clarifying the structure of such topologies.

Suggested Citation

  • Gianni Bosi & Roberto Daris & Gabriele Sbaiz, 2024. "New characterizations of completely useful topologies in mathematical utility theory," Papers 2402.18324, arXiv.org, revised May 2024.
    • Handle: RePEc:arx:papers:2402.18324
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    References listed on IDEAS

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    1. Herden, G., 1991. "Topological spaces for which every continuous total preorder can be represented by a continuous utility function," Mathematical Social Sciences, Elsevier, vol. 22(2), pages 123-136, October.
    2. Bosi, Gianni & Herden, Gerhard, 2019. "The structure of useful topologies," Journal of Mathematical Economics, Elsevier, vol. 82(C), pages 69-73.
    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. Trout Rader, 1963. "The Existence of a Utility Function to Represent Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 229-232.
    5. Gianni Bosi & Magalì Zuanon, 2021. "Topologies for the Continuous Representability of All Continuous Total Preorders," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 420-431, February.
    6. Richter, Marcel K, 1980. "Continuous and Semi-Continuous Utility," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(2), pages 293-299, June.
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