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Continuous Lattices and Domains

Continuous Lattices and Domains

Continuous Lattices and Domains

G. Gierz, University of California, Riverside
K. H. Hofmann, Technische Universität, Darmstadt, Germany
K. Keimel, Technische Universität, Darmstadt, Germany
J. D. Lawson, Louisiana State University
M. Mislove, Tulane University, Louisiana
D. S. Scott, Carnegie Mellon University, Pennsylvania
April 2003
Available
Hardback
9780521803380
CAD$320.95
Hardback
USD
eBook

    Information content and programming semantics are just two of the applications of the mathematical concepts of order, continuity and domains. The authors develop the mathematical foundations of partially ordered sets with completeness properties of various degrees, in particular directed complete ordered sets and complete lattices. Uniquely, they focus on partially ordered sets that have an extra order relation, modelling the notion that one element 'finitely approximates' another, something closely related to intrinsic topologies linking order and topology. Extensive use is made of topological ideas, both by defining useful topologies on the structures themselves and by developing close connections with numerous aspects of topology. The theory so developed not only has applications to computer science but also within mathematics to such areas as analysis, the spectral theory of algebras and the theory of computability. This authoritative, comprehensive account of the subject will be essential for all those working in the area.

    • The only self-contained introduction to the mathematical theory of continuous lattices and domains
    • An authoritative resource for experts and students
    • Based on the authors' classic 'Compendium of Continuous Lattices', bringing together the major developments of the last 21 years

    Reviews & endorsements

    "Although a number of books treating various aspects of domains and continuous lattices have appeared since 1980, none are as up to date and comprehensive as this book. It is and will remain the best resource on continuous lattices, domains, applications, and the vast literature on these topics." Mathematical Reviews

    See more reviews

    Product details

    April 2003
    Hardback
    9780521803380
    628 pages
    236 × 160 × 38 mm
    0.957kg
    Available

    Table of Contents

    • Preface
    • Acknowledgements
    • Foreword
    • Introduction
    • 1. A primer on ordered sets and lattices
    • 2. Order theory of domains
    • 3. The Scott topology
    • 4. The Lawson Topology
    • 5. Morphisms and functors
    • 6. Spectral theory of continuous lattices
    • 7. Compact posets and semilattices
    • 8. Topological algebra and lattice theory: Applications
    • Bibliography
    • List of symbols
    • List of categories
    • Index.
      Authors
    • G. Gierz , University of California, Riverside
    • K. H. Hofmann , Technische Universität, Darmstadt, Germany
    • K. Keimel , Technische Universität, Darmstadt, Germany
    • J. D. Lawson , Louisiana State University
    • M. Mislove , Tulane University, Louisiana
    • D. S. Scott , Carnegie Mellon University, Pennsylvania