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 means of a unique statement an existence result which covers both ways (convexity and acyclicity) of analyzing the problem of existence of maximal elements of non transitive binary relations. And on the other hand, to introduce the concept of an abstract convexity structure, which we call mc-spaces, that generalizes the notion of usual convexity. It is presented as a powerful tool which allows many problems which have only been analyzed (previously) under convexity conditions to be solved.