SAP compactifications of \(n\)-fold and infinite semidirect products
The paper is devoted to the study of semidirect products of semigroups. A semidirect product of an ordered pair of semigroups is generalized to a semidirect product of a sequence (finite or countable) of semigroups. It is proven that the generalized definition has analogous natural properties as the classical one. Finally, the strongly almost periodic compactification of a generalized semidirect product of \(\{S_1, S_2, \dots\}\) is a generalized semidirect product of topological group compactifications of the semigroups \(S_k\) for \(k = 1,2,\dots\).
scientific article; zbMATH DE number 784129