The Continuity of Arens' Product on the Stone-Cech Compactification of Semigroups

Compactifications of semitopological semigroups II

“…(c) // S is a topological semigroup, one would not expect the equality WAP(S) = C(S) always to imply AP(S) = C(S), and indeed this is not the case. Macri (1974) has provided the following EXAMPLE. Let S be an infinite set with distinct elements 1, OES.…”

Abelian semigroups whose Stone-Čech compactifications have left ideal decompositions

“…By definition, sea if and only if seP(t a + ne) for some neZ+. Hence THEOREM [5][6]. The non-periodic, almost cancellative semigroup 'S discussed in this section has property B if and only if R_ x is finite but non-empty.…”

“…Stone-Cech compactifications of semigroups have aroused a good deal of interest recently. Several authors, for example Milnes [6], Marcri [5] and Baker and Butcher [1], have concentrated on problems of the existence of continuous extensions to fiS of the operation in a topological semigroup S. For a discrete semigroup a separately continuous extension always exists, and others such as Pym and Vasudeva [8] have studied the compactifications of particular classes of semigroups. Further interest has centred on the algebraic structure of these compactifications; see for example Hindman [3].…”