ABSTRACT
In this paper the authors discuss some recent work on distributive lattices where they show that the seemingly disparate collection of concepts which forms its title is interrelated, albeit often in a very complicated fashion. They discuss the concept of essential extensions of distributive lattices, which is totally algebraic or even category theoretical in nature. It is a well-known and unfortunate fact that the Dedekind-MacNeille completion of a distributive lattice is no longer distributive in general. The authors construct a completion of a distributive lattice which is not only complete but also is meet continuous and join continuous. The impatient reader need no longer wait for an abstract and general definition of the H-topology.
