Characterization of the existence of maximal elements of acyclic relations |
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Authors: | JC R Alcantud |
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Institution: | (1) Facultad de Economía y Empresa, Universidad de Salamanca, 37008 Salamanca, SPAIN (e-mail: jcr@usal.es) , ES |
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Abstract: | Summary. We obtain a sufficient condition for the existence of maximal elements of irreflexive binary relations that generalizes the
theorem of Bergstrom and Walker by relaxing the compactness condition to a weaker one that is naturally related to the relation.
We then prove that the sufficient conditions used both in the Bergstrom-Walker Theorem and in our generalization provide a
characterization of the existence of maximal elements of acyclic binary relations. Other sufficient conditions for the existence
of maximal elements obtained by Mehta, by Peris and Subiza and by Campbell and Walker are shown to be necessary too.
Received: May 28, 1997; revised version: October 5, 2000 |
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Keywords: | and Phrases: Maximal elements Acyclicity $\succ $-compactness |
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