Davey B.A., Priestley H.A. Introduction to Lattices and Order

2nd Edition. — Cambridge University Press, 2002. — 312 p. — ISBN-1 9780521784511.Ordered structures have been increasingly recognized in recent years due to an explosion of interest in theoretical computer science and all areas of discrete mathematics. This book covers areas such as ordered sets and lattices. A key feature of ordered sets, one which is emphasized in the text, is that they can be represented pictorially. Lattices are also considered as algebraic structures and hence a purely algebraic study is used to reinforce the ideas of homomorphisms and of ideals encountered in group theory and ring theory. Exposure to elementary abstract algebra and the rotation of set theory are the only prerequisites for this text. For the new edition, much has been rewritten or expanded and new exercises have been added.Ordered sets
Lattices and complete lattices
Formal concept analysis
Modular, distributive and Boolean lattices
Representation: the finite case
Congruences
Complete lattices and Galois connections
CPOs and fixpoint theorems
Domains and information systems
Maximality principles
Representation: the general caseAppendix A. a topological toolkit
Appendix B. further reading