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Maximal Elements in Topological Convex Spaces


  • Danilov, V.
  • Sotskov, A.


We introduce axiomatically a more general notion of a convex space dropping one axiom, the so called cancellation law. A wider class of convex sets includes in particular ordinary convex sets and semilattices. Then we introduce a notion of a topological convex space and establish for it theorems like KKM and existence of maximal elements of binary relations.

Suggested Citation

  • Danilov, V. & Sotskov, A., 1998. "Maximal Elements in Topological Convex Spaces," Papiers d'Economie Mathématique et Applications 98.28, Université Panthéon-Sorbonne (Paris 1).
  • Handle: RePEc:fth:pariem:98.28

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    References listed on IDEAS

    1. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    2. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Chateauneuf, Alain & Cohen, Michele, 1994. "Risk Seeking with Diminishing Marginal Utility in a Non-expected Utility Model," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 77-91, July.
    5. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    6. Quiggin John & Wakker Peter, 1994. "The Axiomatic Basis of Anticipated Utility: A Clarification," Journal of Economic Theory, Elsevier, vol. 64(2), pages 486-499, December.
    7. Allais Maurice, 1990. "Cardinal Utility," Journal des Economistes et des Etudes Humaines, De Gruyter, vol. 1(2), pages 1-38, June.
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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General


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