GDL

We provide the first necessary and sufficient conditions in the literature for the existence of maximal


elements in a non-binary choice framework. As an application, the characterization of the existence of


maximal elements for acyclic binary relations obtained in Rodrı ´guez-Palmero and Garcı ´a-Lapresta, 2002,


Mathematical Social Sciences 43, 55–60 [Rodrı ´guez-Palmero, C., Garcı ´a-Lapresta, J.L., 2002. Maximal


elements for irreflexive binary relations on compact sets. Mathematical Social Sciences 43, 55–60], is


deduced as a Corollary. Further characterizations in different settings given by Tian and Zhou, 1995, Journal


of Mathematical Economics 24, 281–303, [Tian, G., Zhou, J., 1995. Transfer continuities, generalizations of


the Weierstrass and maximum theorems: a full characterization. Journal of Mathematical Economics 24,


281–303], follow as well. Analogous characterization problems in the k-acyclic binary cases are solved too.

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