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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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    References listed on IDEAS

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    1. 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.
    2. Herden, Gerhard & Pallack, Andreas, 2002. "Consistency in ordinal data analysis I," Mathematical Social Sciences, Elsevier, vol. 43(1), pages 79-113, January.
    3. 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.
    4. 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.
    5. 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.
    6. Mas-Colell, Andreu, 1975. "A model of equilibrium with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 263-295.
    7. 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.
    8. 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.
    9. 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.
    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. 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.
    12. 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.
    13. 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.
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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. 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. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
    4. 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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