Almost periodic compactifications of semidirect products of flows

Abstract

Let \(S\tilde \times T\) be a semidirect product of semitopological semigroups S and T. If S and T act on topological spaces X and Y, respectively, then under suitable conditions there is a natural action of \(S\tilde \times T\) on X × Y. In this paper we characterize the almost periodic and strongly almost periodic compactification of the flow (\(S\tilde \times T\), X × Y) in terms of related compactifications of (S, X) and (T, Y).