The structure of the overhanging relations associated with some types of closure systems
Over many different kinds of cryptomorphisms equivalent with closure systems (and so with closure operators), we focus here on implication relations and the related overhanging relations, as introduced and axiomatized in a previous paper (Domenach and Leclerc, Math Soc Sci 47(3): 349-366, 2004). In relation with data analysis motivations, we particularize the axioms on overhanging relations in order to account for some types of closure systems, such as nested or distributive ones. We also examine the lattice structure of overhanging relations, which is isomorphic to the lattice of closure systems, and derived structures for particular sets of overhangings.
closure system implication distributivity tree of subsets