Introduction to Lattices and Order

by B. A. Davey, H. A. Priestley

Overview

This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.

Product Details

ISBN-13:	9781107713536
Publisher:	Cambridge University Press
Publication date:	04/18/2002
Sold by:	Barnes & Noble
Format:	eBook
File size:	20 MB
Note:	This product may take a few minutes to download.

Table of Contents

Preface; Preface to the first edition; 1. Ordered sets; 2. Lattices and complete lattices; 3. Formal concept analysis; 4. Modular, distributive and Boolean lattices; 5. Representation theory: the finite case; 6. Congruences; 7. Complete lattices and Galois connections; 8. CPOs and fixpoint theorems; 9. Domains and information systems; 10. Maximality principles; 11. Representation: the general case; Appendix A. A topological toolkit; Appendix B. Further reading; Notation index; Index.

Editorial Reviews

This second edition of a text devoted to ordered sets and lattices and their contemporary applications presents a reorganization and updating of the content of the first (1990) edition. There is a fresh treatment of fixpoint theorems and more emphasis on Galois connections. New exercises have also been added to this edition. Written for advanced undergraduate and first-year graduate students, the book requires background in abstract algebra and the notation of set theory. Davey is affiliated with La Trobe University. Priestley is affiliated with the University of Oxford. Annotation c. Book News, Inc., Portland, OR (booknews.com)

"...this second edition merits the same five stars as the first."
Mathematical Reviews


"The book is written in a very engaging and fluid style. The understanding of the content is aided tremendously by the very large number of beautiful lattice diagrams...The book provides a wonderful and accessible introduction to lattice theory, of equal interest to both computer scientists and mathematicians."
Jonathan Cohen, SIGACT News

From the Publisher