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Utility Theory and Continuous Monotonic Functions

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  • Beardon, Alan F

Abstract

We examine the continuity of maps between linearly ordered spaces and apply the results to utility functions representing preference relations. In particular, we show that the continuous function constructed by Debreu is, in essence, unique.

Suggested Citation

  • Beardon, Alan F, 1994. "Utility Theory and Continuous Monotonic Functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(4), pages 531-538, May.
    • Handle: RePEc:spr:joecth:v:4:y:1994:i:4:p:531-38
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    Cited by:

    1. 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.
    2. Caserta, A. & Giarlotta, A. & Watson, S., 2008. "Debreu-like properties of utility representations," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1161-1179, December.
    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.
    4. Candeal, Juan C. & Indurain, Esteban & Mehta, Ghanshyam B., 1996. "Further remarks on totally ordered representable subsets of Euclidean space," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 381-390.

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