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A characterization of compactness through preferences

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  • Gutiérrez, José Manuel

Abstract

The existence of an optimal solution of the standard decision problem can characterize the compactness of the feasible set. It is proved that the feasible set is compact if and only if there is a maximal element for any upper semicontinuous preference. Here "preference" means asymmetric and negatively transitive binary relation.

Suggested Citation

  • Gutiérrez, José Manuel, 2009. "A characterization of compactness through preferences," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 131-133, January.
    • Handle: RePEc:eee:matsoc:v:57:y:2009:i:1:p:131-133
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    References listed on IDEAS

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    1. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
    2. Candeal, Juan C. & Indurain, Esteban & Mehta, Ghanshyam B., 2004. "Utility functions on locally connected spaces," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 701-711, September.
    3. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
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