Connective Segmentation Generalized to Arbitrary Complete Lattices

Abstract

We begin by defining the setup and the framework of connective segmentation. Then we start from a theorem based on connective criteria, established for the power set of an arbitrary set. As the power set is an example of a complete lattice, we formulate and prove an analogue of the theorem for general complete lattices. Secondly, we consider partial partitions and partial connections. We recall the definitions, and quote a result that gives a characterization of (partial) connections. As a continuation of the work in the first part, we generalize this characterization to complete lattices as well. Finally we link these two approaches by means of a commutative diagram, in two manners.