A unified view of the existence of maximals

Federico Quartieri

Journal of Mathematical Economics, 2022, vol. 99, issue C

Abstract: The paper examines the conditions for the existence of maximals of a relation on every nonempty compact subset of its ground set. A preliminary analysis shows that the existence of maximals of a Suzumura-consistent relation is implied by the existence of maximals of the right trace of its transitive closure. Building on this fact, various theorems of the literature are unified by identifying a common topological 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 cases of interest to economics. Finally, a necessary and sufficient condition is presented for the existence of maximals on every nonempty compact subset of the ground set of a relation.

Keywords: Maximal; Existence; Right trace; Suzumura-consistency (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304406821001634
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:99:y:2022:i:c:s0304406821001634

DOI: 10.1016/j.jmateco.2021.102609

Access Statistics for this article

Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii

More articles in Journal of Mathematical Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().