Algebra in the Stone-Cech Compactification

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.