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Synopsis
This is the first introductory textbook on ordered sets and lattices, and covers both the basic theory and its applications. The importance of ordered structures has been increasingly recognised in recent years due to an explosion of interest in computer science and all areas of discrete mathematics. The authors provide a thorough introduction to ordered sets, lattices, distributive lattices and Boolean algebras. Ordered sets, and in particular lattices, can be represented pictorially, and this key feature is emphasised throughout. Lattices are also considered as algebraic structures and their study from this viewpoint reinforces ideas encountered in the theory of groups and rings. The representation of distributive lattices by ordered topological spaces is presented; a self-contained treatment of the requisite topology is included. Two chapters are devoted to topics with application to computer science. These cover complete partial orders, domains (including their relation to information systems), and fixpoint theory. Another chapter deals with formal concept analysis - a new and important application of lattice theory of interest to mathematicians and social scientists. Prerequisites are minimal; all that is assumed is exposure to the notation of set theory and elementary abstract algebra. The numerous classroom-tested exercises will make the book especially useful for course accompaniment, but it will also be valuable as a background reference for mathematicians, logicians and computer scientists.
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Review
"Recommended for every academic mathematics collection." Choice ."..it will surely become a classic." Mathematical Reviews ."..remains a first choice for a textbook on lattices and ordered sets." Joel Berman, Australian Mathematical Society Gazette
Book Description
The explosive development of theoretical computer science in recent years has influenced this new edition: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added.
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- PublisherCambridge University Press
- Publication date1990
- ISBN 10 0521367662
- ISBN 13 9780521367660
- BindingPaperback
- LanguageEnglish
- Number of pages256
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Introduction to Lattices and Order
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Cambridge University Press, 1990
ISBN 10: 0521367662
ISBN 13: 9780521367660
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Introduction to Lattices and Order
Published by
Cambridge University Press, 1990
ISBN 10: 0521367662
ISBN 13: 9780521367660
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ISBN 13: 9780521367660
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Introduction to Lattices and Order
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ISBN 13: 9780521367660
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Introduction to Lattices and Order
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ISBN 13: 9780521367660
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