Regular idempotents in 𝛽𝑆
Yevhen Zelenyuk · Transactions of the American Mathematical Society · 2010
Let S S be a discrete semigroup and let β S \beta S be the Stone-Čech compactification of S S . We take the points of β S \beta S to be the ultrafilters on S S . Being a compact Hausdorff right topological semigroup, β S \beta S has idempotents. Every idempotent p ∈ β S p\in \beta S determines a left invariant topology T p \mathcal {T}_p on S S with a neighborhood base at a ∈ S a\in S consisting of subsets a B ∪ { a } aB\cup \{a\} , where B ∈ p B\in p . If S S is a group and p p is an idempotent in S ∗