Algebra in the Stone-Cech Compactification : : Theory and Applications / / Neil Hindman, Dona Strauss.

• Superior document: Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1
• VerfasserIn: Hindman, Neil,; Strauss, Dona,
• MitwirkendeR: Hindman, Neil,; Strauss, Dona,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2011]; ©2012
• Year of Publication: 2011
• Edition: 2nd rev. and ext. ed.
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (591 p.)

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.

Table of Contents

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