Lattice theorynvolume 1, Special topics and applications

Description

George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer 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 Grätzer and Joseph P. S. Kung. Part III. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich Wehrung and George Grätzer Front Matter....Pages i-xiii Front Matter....Pages 1-3 Continuous and Completely Distributive Lattices....Pages 5-53 Frames: Topology Without Points....Pages 55-88 Front Matter....Pages 89-89 Planar Semimodular Lattices: Structure and Diagrams....Pages 91-130 Planar Semimodular Lattices: Congruences....Pages 131-165 Sectionally Complemented Lattices....Pages 167-194 Combinatorics in finite lattices....Pages 195-229 Front Matter....Pages 231-233 Schmidt and Pudlák’s Approaches to CLP....Pages 235-296 Congruences of lattices and ideals of rings....Pages 297-335 Liftable and Unliftable Diagrams....Pages 337-392 Two More Topics on Congruence Lattices of Lattices....Pages 393-435 Back Matter....Pages 437-468