George Gratzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Gratzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This first volume is divided into three parts. Part I. Topology and Lattices includes two chapters by Klaus Keimel, Jimmie Lawson and Ales Pultr, Jiri Sichler. Part II. Special Classes of Finite Lattices comprises four chapters by Gabor Czedli, George Gratzer and Joseph P. S. Kung. Part III. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich Wehrung and George Gratzer.
George Gratzer, Member of the Canadian Academy of Sciences and Foreign Member of the Hungarian Academy of Sciences, is the author of 26 books in five languages and about 260 articles, most of them on his research in lattice theory. Friedrich Wehrung is professor at the University of Caen and an associate editor for Algebra Universalis, a mathematical journal devoted to universal algebra and lattice theory. He is the author of numerous publications in the field and wrote an appendix to the second edition of Gratzer's General Lattice Theory.
Introduction. Part I Topology and Lattices.- Chapter 1. Continuous and Completely Distributive Lattices.- Chapter 2. Frames: Topology Without Points.- Part II. Special Classes of Finite Lattices.- Chapter 3. Planar Semi modular Lattices: Structure and Diagram.- Chapter 4. Planar Semi modular Lattices: Congruences.- Chapter 5. Sectionally Complemented Lattices.- Chapter 6. Combinatorics in finite lattices.- Part III. Congruence Lattices of Infinite Lattices and Beyond.- Chapter 7. Schmidt and Pudlak's Approaches to CLP.- Chapter 8. Congruences of lattices and ideals of rings.- Chapter 9. Liftable and Unliftable Diagrams.- Chapter 10. Two topics related to congruence lattices of lattices.