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Format: 1 online resource (591 p.)

Edition: 2nd rev. and ext. ed.

ISBN: 9783110258356 , 9783110238570

Series Statement: De Gruyter Textbook

Content: This is the second revised and extended edition of the successful book on the algebraic structure of the Stone-Čech 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.

Note: 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- Čech Compactification of a Discrete Space -- , Chapter 4. ßS - The Stone-Čech 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 , Mode of access: Internet via World Wide Web. , In English.

In: DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570

In: DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471

In: DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205

In: E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2011, De Gruyter, 9783110261189

In: E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2011, De Gruyter, 9783110261233

In: E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2011, De Gruyter, 9783110261202

Additional Edition: ISBN 9783110256239

Language: English

Subjects: Mathematics

DOI: 10.1515/9783110258356

URL: https://doi.org/10.1515/9783110258356

URL: https://www.degruyter.com/isbn/9783110258356

URL: Cover