Algebra in the Stone-Cech Compactification

Theory and Applications
2. revidierte and ext. Auflage 2011
ISBN: 978-3-11-025623-9
Verlag: De Gruyter

Buch, Englisch, 591 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 1023 g

Reihe: De Gruyter Textbook

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.

Autoren/Hrsg.

Strauss, Dona

Hindman, Neil

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

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

Über Autor(innen)

Hindman, Neil
Neil Hindman, Howard University, Washington, USA.

Strauss, Dona
Dona Strauss, University of Leeds, UK.

Neil Hindman, Howard University, Washington, D.C., USA; Dona Strauss, University of Leeds, United Kingdom.