Topological Duality for Distributive Lattices: Theory and Applications

Abstract

This book is a course in Stone-Priestley duality theory, with applications to logic and theoretical computer science. Our target audience are graduate students and researchers in mathematics and computer science. Our aim is to get in a fairly full palette of duality tools as directly and quickly as possible, then to illustrate and further elaborate these tools within the setting of three emblematic applications: semantics of propositional logics, domain theory in logical form, and the theory of profinite monoids for the study of regular languages and automata.

arXiv commentThis material will be published by Cambridge University Press as "Topological Duality for Distributive Lattices: Theory and Applications" by Mai Gehrke and Sam van Gool. This pre-publication is free to view and download for personal use only. Not for re-distribution, re-sale, or use in derivative works. (c) 2023 Mai Gehrke and Sam van Gool