Algebra in the Stone-Cech Compactification: Theory and Applications (De Gruyter Expositions in Mathematics, 27)

This work presents a study of the algebraic properties of compact right topological semigroups in general and the Stone-Cech compactification of a discrete semigroup in particular. Several powerful applications to combinatorics, primarily to the branch of combinarotics known as Ramsey Theory, are given, and connections with topological dynamics and ergodic theory are presented. The text is essentially self-contained and does not assume any prior mathematical expertise beyond a knowledge of the basic concepts of algebra, analysis and topology, as usually covered in the first year of graduate school. Most of the material presented is based on results that have so far only been available in research journals. In addition, the book contains a number of new results that have so far not been published elsewhere. The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, BrasilWalter D. Neumann, Columbia University, New York, USAMarkus J. Pflaum, University of Colorado, Boulder, USADierk Schleicher, Aix-Marseille Université, FranceKatrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021) By Neil Hindman, Dona Strauss. Includes Bibliographical References And Index.