Contact relations on bounded distributive lattices and related structures

Abstract

We study a discrete representation of contact relations on bounded distributive lattices and some of their reducts. In the course of the paper, we apply ideas and techniques developed by Ivo D\"untsch, Dimiter Vakarelov, and Michael Winter, and we show---among others---that contact relations on a distributive join semi-lattice $L$ with the bottom element correspond to reflexive and symmetric relations which are closed in the product of the Stone space of $L$.