This book, now in its second revised and extended edition, is a self-contained exposition of the theory of compact right semigroupsfor 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.

Autorentext

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

Klappentext

This is the second edition of the successful book on the algebraic structure of the Stone-ech compactification of a discrete semigroup and its applications, primarily in Ramsey Theory and in topological dynamics. There has been very active research in the subject dealt with by the book in the past thirteen years. Thus the first edition has been updated by including proofs of some of the more accessible recent advances and describing some of the others in the notes, as well as expanding the bibliography.

This book is an almost self-contained exposition of the theory of compact right topological semigroups, with particular emphasis on the Stone-ech compactification of a discrete semigroup and its algebraic properties. 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 Finite Sums Theorem, van der Waerden's Theorem, the Central Sets Theorem, partition regularity of matrices, multidimensional Ramsey theory, and many more.

Zusammenfassung

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