Continuous lattices and domains

G. Gierz ... [et al.]

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.

「Nielsen BookData」より

[目次]

  • 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.

「Nielsen BookData」より

この本の情報

書名 Continuous lattices and domains
著作者等 Gierz, Gerhard
Hofmann K. H. (Technische Universitat Darmstadt Germany)
Keimel Klaus
Lawson J.D. (Louisiana State University)
Mislove Michael W.
Scott D. S. (Carnegie Mellon University Pennsylvania)
Gierz G.
シリーズ名 Encyclopedia of mathematics and its applications
出版元 Cambridge University Press
刊行年月 2003
ページ数 xxxvi, 591 p.
大きさ 24 cm
ISBN 0521803381
NCID BA61442367
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言語 英語
出版国 イギリス
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