UNIFIED TREATMENT OF THE PROBLEM OF EXISTENCE OF MAXIMAL ELEMENTS IN BINARY RELATIONS - A CHARACTERIZATION

The aim of this. paper is twofold. On the one hand, to present by mean s of a unique statement, an existence result that covers both ways (co nvexity and acyclicity) of analyzing the problem of the existence of m aximal elements in non-transitive binary relations. On the other hand, to introduce the concept of an abstract convexity structure, which we call me-spaces, that generalizes the notion of usual convexity. It is presented as a powerful tool that allows many problems that have only been analyzed (previously) under convexity conditions to be solved. ( C) 1998 Elsevier Science S.A.