Introduction to Lattices and Order
Cambridge University Press
Edition: 2, 4/18/2002
EAN 9780521784511, ISBN10: 0521784514
Paperback, 312 pages, 22.9 x 15.2 x 1.8 cm
Language: English
Originally published in English
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.
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.