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Open gaps, metrization and utility

Author

Listed:
  • Gerhard Herden

    (Department of Mathematics and Computer Science, University of Essen, D-45117 Essen, GERMANY)

  • Ghanshyam B. Mehta

    (Department of Economics, University of Queensland, St. Lucia, Qld. 4067, AUSTRALIA)

Abstract

It is shown that each of the Debreu Open Gap Theorem and the Debreu Continuous Utility Representation Theorem can be used in order to prove the other. Furthermore, it is proved that the classical Alexandroff-Urysohn Metrization Theorem implies Debreu's Continuous Utility Representation Theorem and, thus, all known results on the existence of continuous utility functions.

Suggested Citation

  • Gerhard Herden & Ghanshyam B. Mehta, 1996. "Open gaps, metrization and utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 541-546.
    • Handle: RePEc:spr:joecth:v:7:y:1996:i:3:p:541-546
    Note: Received: August 24, 1993; revised version March 28, 1994
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    Cited by:

    1. J. Alcantud & G. Bosi & M. Campión & J. Candeal & E. Induráin & C. Rodríguez-Palmero, 2008. "Continuous Utility Functions Through Scales," Theory and Decision, Springer, vol. 64(4), pages 479-494, June.
    2. Herden, G. & Mehta, G. B., 2004. "The Debreu Gap Lemma and some generalizations," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 747-769, November.
    3. Jose C. R. Alcantud & Ghanshyam B. Mehta, 2005. "Constructive Utility Functions on Banach spaces," Microeconomics 0502003, University Library of Munich, Germany.
    4. 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.

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