Articoli correlati a Introduction to Lattices and Order
Sinossi
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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Contenuti
1. Ordered sets; 2. Special types of ordered set; 3. Lattices as algebraic structures; 4. Boolean algebras; 5. The structure of finite distributive lattices and finite Boolean algebras; 6. Ideals, filters, and congruences; 7. The Stone Representation Theorem for Boolean algebras; 8. Lattices in algebra; Appendix: outline of relevant basic topology.
Product Description
Book by Davey B A Priestley H A
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
- EditoreCambridge University Press
- Data di pubblicazione1990
- ISBN 10 0521365848
- ISBN 13 9780521365840
- RilegaturaCopertina rigida
- LinguaInglese
- Numero edizione1
- Numero di pagine256
- Contatto del produttorenon disponibile
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Introduction to Lattices and Order
Editore:
Cambridge University Press, 1990
ISBN 10: 0521365848
ISBN 13: 9780521365840
Antico o usato
Rilegato
Da: Barnaby, Oxford, Regno Unito
Valutazione del venditore 4 su 5 stelle
Hardcover. Condizione: Good. Former academic library book; ink stamps to endpapers; spine label and shelf number to spine. Dust jacket absent. Top edge a bit greyed with dust. Pages free from notes or highlighting. Otherwise, sound and serviceable. Publisher's note: 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. Size: 23.6 x 15.7 x 2 cm. viii, 248 pp. Shipped Weight: Under 1 kilo. Category: Mathematics; Ordered sets; Lattice theory; ISBN: 0521365848. ISBN/EAN: 9780521365840. Add. Inventory No: 250618WCY0906042. Codice articolo 250618WCY0906042
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