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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The importance of ordered structures is addressed here. 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. Exposure to elementary abstract algebra and the rotation of set theory are the only prerequisites for this text, intended primarily as a textbook. The level is suitable for advanced undergraduates and first year graduate students.For the new edition, much has been rewritten or expanded and new exercises have been added.Review:
."..remains a first choice for a textbook on lattices and ordered sets." Joel Berman, Australian Mathematical Society Gazette
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Descripción Cambridge University Press, 1990. Paperback. Estado de conservación: New. Nº de ref. de la librería P110521367662
Descripción Cambridge University Press. PAPERBACK. Estado de conservación: New. 0521367662 New Condition. Nº de ref. de la librería NEW6.1182580
Descripción Cambridge University Press, 1990. Paperback. Estado de conservación: New. Nº de ref. de la librería DADAX0521367662
Descripción Estado de conservación: Brand New. Book Condition: Brand New. Nº de ref. de la librería 97805213676601.0