This is the second revised and extended edition of the successful book on the algebraic structure of the Stone-Cech compactification of a discrete semigroup and its combinatorial applications, primarily in the field known as Ramsey Theory. There has been very active research in the subject dealt with by the book in the 12 years which is now included in this edition. This book is a self-contained exposition of the theory of compact right semigroups for discrete semigroups and the algebraic properties of these objects. The methods applied in the book constitute a mosaic of infinite combinatorics, algebra, and topology. The reader will find numerous combinatorial applications of the theory, including the central sets theorem, partition regularity of matrices, multidimensional Ramsey theory, and many more.
Rezensionen / Stimmen
"The present book is the first devoted to an extensive study of the algebraic structure of ßS and the many applications thereof; it is an exciting book, written - and very well written - by two mathematicians who are eminently qualified two write it, and it is essentially self-contained, requiring only that the reader come to it with the basic concepts of first graduate courses in algebra, analysis and topology. [.] I recommend this book highly; it will be very useful, both to researchers and to students. Its index, list of symbols and up-to-date bibliography are very helpful [.]."
Paul Milnes, Zentralblatt MATH / 1998
"The authors present a self-contained exposition [.]. The book under review is written by two mathematicians who have contributed in a decisive way to this rapidly expanding area [.] and provides a unique opportunity to obtain a 'colorful' panoramic view of the subject."
Michael Tkacenko, MathSciNet / 1999
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
US School Grade: From College Freshman to College Senior
Editions-Typ
Maße
Höhe: 240 mm
Breite: 170 mm
Dicke: 33 mm
Gewicht
ISBN-13
978-3-11-025623-9 (9783110256239)
Schweitzer Klassifikation
Neil Hindman, Howard University, Washington, D.C., USA; Dona Strauss, University of Leeds, United Kingdom.
Frontmatter
Preface to the First Edition
Preface to the Second Edition
Notation
Contents
Part I. Background Development
Chapter 1. Semigroups and Their Ideals
Chapter 2. Right Topological (and Semitopological and Topological) Semigroups
Chapter 3. ßD-Ultrafilters and The Stone- Cech Compactification of a Discrete Space
Chapter 4. ßS - The Stone-Cech Compactification of a Discrete Semigroup
Chapter 5. ßS and Ramsey Theory - Some Easy Applications
Part II. Algebra of ßS
Chapter 6. Ideals and Commutativity in ßS
Chapter 7. Groups in ßS
Chapter 8. Cancellation
Chapter 9. Idempotents
Chapter 10. Homomorphisms
Chapter 11. The Rudin-Keisler Order
Chapter 12. Ultrafilters Generated by Finite Sums
Chapter 13. Multiple Structures in ßS
Part III Combinatorial Applications
Chapter 14. The Central Sets Theorem
Chapter 15. Partition Regularity of Matrices
Chapter 16. IP, IP*, Central, and Central* Sets
Chapter 17. Sums and Products
Chapter 18. Multidimensional Ramsey Theory
Part IV. ConnectionsWith Other Structures
Chapter 19. Relations With Topological Dynamics
Chapter 20. Density - Connections with Ergodic Theory
Chapter 21. Other Semigroup Compactifications
Bibliography
Index
