General solutions for choice sets: The Generalized Optimal-Choice Axiom set

In this paper we characterize the existence of best choices of arbitrary binary relations over non finite sets of alternatives, according to the Generalized Optimal-Choice Axiom condition introduced by Schwartz. We focus not just in the best choices of a single set X, but rather in the best choices of all the members of a family K of subsets of X. Finally we generalize earlier known results concerning the existence (or the characterization) of maximal elements of binary relations on compact subsets of a given space of alternatives.