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The Debreu Gap Lemma and some generalizations

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  • Herden, G.
  • Mehta, G. B.

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  • 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.
    • Handle: RePEc:eee:mateco:v:40:y:2004:i:7:p:747-769
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    1. Mas-Colell, Andreu, 1975. "A model of equilibrium with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 263-295.
    2. 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.
    3. 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.
    4. Wakker, Peter, 1988. "Continuity of Preference Relations for Separable Topologies," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 105-110, February.
    5. Beardon, Alan F. & Candeal, Juan C. & Herden, Gerhard & Indurain, Esteban & Mehta, Ghanshyam B., 2002. "The non-existence of a utility function and the structure of non-representable preference relations," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 17-38, February.
    6. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    7. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Beardon, A. F. & Mehta, G. B., 1994. "Utility functions and the order type of the continuum," Journal of Mathematical Economics, Elsevier, vol. 23(4), pages 387-390, July.
    9. 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.
    10. 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.
    11. Herden, Gerhard & Mehta, Ghanshyam B, 1996. "Open Gaps, Metrization and Utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 541-546, April.
    12. Herden, Gerhard & Pallack, Andreas, 2002. "Consistency in ordinal data analysis I," Mathematical Social Sciences, Elsevier, vol. 43(1), pages 79-113, January.
    13. Monteiro, Paulo Klinger, 1987. "Some results on the existence of utility functions on path connected spaces," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 147-156, April.
    14. Beardon, Alan F & Mehta, Ghanshyam B, 1994. "The Utility Theorems of Wold, Debreu, and Arrow-Hahn," Econometrica, Econometric Society, vol. 62(1), pages 181-186, January.
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    Cited by:

    1. 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.
    2. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
    3. 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.
    4. Knoblauch, Vicki, 2023. "Lexicographic preference representation: Intrinsic length of linear orders on infinite sets," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    5. Bosi, Gianni & Herden, Gerhard, 2014. "Topological spaces for which every closed and semi-closed preorder respectively admits a continuous multi-utility representation," MPRA Paper 53404, University Library of Munich, Germany.

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