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Continuous utility on connected separable topological spaces

Author

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  • Yann Rébillé

    (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - IEMN-IAE Nantes - Institut d'Économie et de Management de Nantes - Institut d'Administration des Entreprises - Nantes - UN - Université de Nantes)

Abstract

The elaboration of utility theory takes back its source in early economic theory. Despite an obvious practical use for applications and an intuitive appeal, utility theory relies on sophisticated abstract mathematics such as topology. Our interest is primarily on Debreu–Eilenberg’s theorem. On connected separable topological spaces continuous total preorders admit continuous utility representations. We provide a simple proof and derive related results.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Yann Rébillé, 2019. "Continuous utility on connected separable topological spaces," Post-Print hal-03727641, HAL.
    • Handle: RePEc:hal:journl:hal-03727641
    DOI: 10.1007/s40505-018-0149-4
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    References listed on IDEAS

    as
    1. Herden, G., 1989. "On the existence of utility functions," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 297-313, June.
    2. Herden, G., 1989. "On the existence of utility functions ii," Mathematical Social Sciences, Elsevier, vol. 18(2), pages 107-117, October.
    3. Schmeidler, David, 1971. "A Condition for the Completeness of Partial Preference Relations," Econometrica, Econometric Society, vol. 39(2), pages 403-404, March.
    4. Mehta, Ghanshyam, 1988. "Some general theorems on the existence of order-preserving functions," Mathematical Social Sciences, Elsevier, vol. 15(2), pages 135-143, April.
    5. Jaffray, Jean-Yves, 1975. "Existence of a Continuous Utility Function: An Elementary Proof," Econometrica, Econometric Society, vol. 43(5-6), pages 981-983, Sept.-Nov.
    6. Mehta, Ghanshyam, 1977. "Topological Ordered Spaces and Utility Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 779-782, October.
    7. Herden, G., 1995. "On some equivalent approaches to Mathematical Utility Theory," Mathematical Social Sciences, Elsevier, vol. 29(1), pages 19-31, February.
    8. 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.
    9. George J. Stigler, 1950. "The Development of Utility Theory. II," Journal of Political Economy, University of Chicago Press, vol. 58(5), pages 373-373.
    10. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
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    Cited by:

    1. Gianni Bosi & Magalì Zuanon, 2020. "Topologies for the continuous representability of every nontotal weakly continuous preorder," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 369-378, October.
    2. M. Ali Khan & Metin Uyanık, 2021. "Topological connectedness and behavioral assumptions on preferences: a two-way relationship," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 411-460, March.
    3. 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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    More about this item

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D60 - Microeconomics - - Welfare Economics - - - General
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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