Introduction to lattices and order

B.A. Davey, H.A. Priestley

This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.

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[目次]

  • Preface
  • Preface to the first edition
  • 1. Ordered sets
  • 2. Lattices and complete lattices
  • 3. Formal concept analysis
  • 4. Modular, distributive and Boolean lattices
  • 5. Representation theory: the finite case
  • 6. Congruences
  • 7. Complete lattices and Galois connections
  • 8. CPOs and fixpoint theorems
  • 9. Domains and information systems
  • 10. Maximality principles
  • 11. Representation: the general case
  • Appendix A. A topological toolkit
  • Appendix B. Further reading
  • Notation index
  • Index.

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この本の情報

書名 Introduction to lattices and order
著作者等 Davey, Brian Albert
Priestley, Hilary Ann
Priestley H. A.
Davey B. A.
出版元 Cambridge University Press
刊行年月 2002
版表示 2nd ed
ページ数 xii, 298 p.
大きさ 23 cm
ISBN 9780521784511
NCID BA56326822
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言語 英語
出版国 イギリス
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