Algebra in the Stone-Čech compactification: theory and applications
"This is the second revised and extended edition of the successful book on the algebraic structure of the Stone-C̆ech 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 prop…
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- Full title :Algebra in the Stone-Čech compactification : theory and applications / Neil Hindman, Donna Strauss.
Summary
"This is the second revised and extended edition of the successful book on the algebraic structure of the Stone-C̆ech 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."--Publisher's website.
Read More ↓Edition Statements
- Publication Date:©2012.
- Edition:2nd rev. and extended ed
Publication Statements
- Publisher(s):De Gruyter
- Place of Publication:Berlin
- Language:eng
- Publication Date:©2012.
The Physical Object
- Description:xvii, 591 pages ; : 25 cm.
Edition Identifiers
- ISBN:9783110256239, 3110256231, 9783110258356, 3110258358
- oclc:ocn754186859
- LC Classification:QA611.23
- Dewey Decimal:514/.32
Table of Contents
Part I. Background Development. Semigroups and Their Ideals ; Right Topological (and Semitopological and Topological) Semigroups ; ßD-Ultrafilters and The Stone- C̆ech Compactification of a Discrete Space ; ßS -- The Stone-C̆ech Compactification of a Discrete Semigroup ; ßS and Ramsey Theory -- Some Easy Applications. -- Part II. Algebra of ßS. Ideals and Commutativity in ßS ; Groups in ßS ; Cancellation ; Idempotents ; Homomorphisms ; The Rudin-Keisler Order ; Ultrafilters Generated by Finite Sums ; Multiple Structures in ßS. -- Part III Combinatorial Applications. The Central Sets Theorem ; Partition Regularity of Matrices ; IP, IP*, Central, and Central* Sets ; Sums and Products ; Multidimensional Ramsey Theory. -- Part IV. Connections With Other Structures. Relations With Topological Dynamics ; Density -- Connections with Ergodic Theory ; Other Semigroup Compactifications.
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The Stone-Cech compactification
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