Lattice Theory: Special Topics and Applications

1. Front Matter

   Pages i-xiii

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2. Topology and Lattices

   1. Front Matter

      Pages 1-3

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   2. Continuous and Completely Distributive Lattices

      • Klaus Keimel, Jimmie Lawson

      Pages 5-53

   3. Frames: Topology Without Points

      • Aleš Pultr, Jiří Sichler

      Pages 55-88

3. Special Classes of Finite Lattices

   1. Front Matter

      Pages 89-89

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   2. Planar Semimodular Lattices: Structure and Diagrams

      • Gábor Czédli, George Grätzer

      Pages 91-130

   3. Planar Semimodular Lattices: Congruences

      • George Grätzer

      Pages 131-165

   4. Sectionally Complemented Lattices

      • George Grätzer

      Pages 167-194

   5. Combinatorics in finite lattices

      • Joseph P. S. Kung

      Pages 195-229

4. Congruence Lattices of Infinite Lattices, and Beyond

   1. Front Matter

      Pages 231-233

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   2. Schmidt and Pudlák’s Approaches to CLP

      • Friedrich Wehrung

      Pages 235-296

   3. Congruences of lattices and ideals of rings

      • Friedrich Wehrung

      Pages 297-335

   4. Liftable and Unliftable Diagrams

      • Friedrich Wehrung

      Pages 337-392

   5. Two More Topics on Congruence Lattices of Lattices

      • George Grätzer

      Pages 393-435

5. Back Matter

   Pages 437-468

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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.

• combinatorics
• congruence lattice
• finite lattice
• lattice theory
• topology

• Department of Mathematics, University of Manitoba, Winnipeg, Canada

  George Grätzer

• Department of Mathematics, University of Caen, Caen, France

  Friedrich Wehrung

George Grätzer, 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 Grätzer's General Lattice Theory.

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