The relationships among many notions of largeness for subsets of a semigroup
A set \(A\subset \mathbb N\) is called \textit{thick} if it contains arbitrarily long integer intervals. The set \(A\) is \textit{syndetic} if it has bounded gaps; it is called \textit{an \(AP\)-set} if it contains arbitrarily long arithmetic progressions. The authors define analogues of these concepts for an abitrary semigroup \(S\) together with quite a few other notions which somehow embody the idea of a large subset of \(S\). They also consider \(S\) with the discrete topology and study the introduced notions in the context of \(\beta S\) providing, among other things, some combinatorial characterizations as well as the implications and counterexamples to decribe relationships between these large subsets of \(S\).
scientific article; zbMATH DE number 7080901