Algebra in the Stone–Čech Compactification: An Update - Hindman, Neil; Strauss, Dona (Topology Proceedings, 2024)
The first edition of Algebra in the Stone-Čech Compactification was published in 1998 and the second edition in 2012. Since that time there have been many new results published about the algebraic structure of the Stone-Čech compactification β S of the discrete semigroup S and the combinatorial applications of that structure, mostly in the area of Ramsey theory. We present here, with proofs so far as possible, what we believe to be some of the most significant of these new results.