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Transfer Method for Characterizing the Existence of Maximal Elements of Binary Relations on Compact or Noncompact Sets

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  • Tian, Guoqiang
  • Zhou, Jianxin

Abstract

This paper systematically studies the existence of maximal elements for unordered binary relation on compact or noncompact sets in a general topological space. This is done by developing a method, called transfer method, to derive various necessary and sufficient conditions that characterize the existence of maximal elements for a binary relation in terms of:(1) (generalized) transitivity conditions under certain topological assumptions;(2) topological conditions under certain (generalized) transitivity assumptions; and (3) (generalized)convexity conditions under certain topological assumptions. There are two basic approaches in the literature to prove the existence by providing sufficient conditions. One assumes certain convexity and continuity conditions for a topological vector space and the other assumes certain weakened transitivity and continuity conditions for a general topological space. The results unify those two approaches and generalize almost all of the existing results in literature.

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File URL: http://mpra.ub.uni-muenchen.de/41227/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 41227.

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Date of creation: 1992
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Publication status: Published in SIAM Journal on Optimization 3.2(1992): pp. 360-375
Handle: RePEc:pra:mprapa:41227

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Related research

Keywords: Binary relations; maximal elements; transfer continuities; transfer transitivities; transfer convexities;

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Cited by:
  1. Rodriguez-Palmero, Carlos & Garcia-Lapresta, Jose-Luis, 2002. "Maximal elements for irreflexive binary relations on compact sets," Mathematical Social Sciences, Elsevier, Elsevier, vol. 43(1), pages 55-60, January.
  2. Leandro Nascimento, 2011. "Remarks on the consumer problem under incomplete preferences," Theory and Decision, Springer, Springer, vol. 70(1), pages 95-110, January.
  3. Begoña Subiza, 2000. "A Kkm-Result And An Application For Binary And Non-Binary Choice Functions," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2000-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  4. Tian, Guoqiang, 2010. "On the Existence of Price Equilibrium in Economies with Excess Demand Functions," MPRA Paper 57930, University Library of Munich, Germany, revised Jul 2014.

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