Existence of maximals via right traces

Federico Quartieri

MPRA Paper from University Library of Munich, Germany

Abstract: This paper examines the conditions for the existence of a maximal element of a relation on every nonempty compact subset of its ground set. A preliminary analysis establishes some connections between the maximals of a relation and those of its right trace. Via this analysis, various results of the literature are unified by identifying a common property of their assumptions that concerns the right trace of the transitive closure of the objective relation. Next, a generalization is provided so as to accommodate some relations of interest to economics. Finally, a necessary and sufficient condition is presented for the existence of a maximal on every nonempty compact subset of the ground set of a relation.

Keywords: Maximal element; Existence; Right trace; Transitive closure; Suzumura-consistency. (search for similar items in EconPapers)
JEL-codes: C60 C61 D11 (search for similar items in EconPapers)
Date: 2021-04-15
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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