Certain Finitely Generated Compact Zero Dimensional Semigroups
Robert P. Hunter · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1988
Abstract Consider a compact zero dimensional (profinite) monoid. While the group of units must be open, a regular D-class need not be open in the ideal it generates. This is the case if and only if the semigroup contains infinitely many copies of a certain semilattice composed of an increasing sequence of idempotents converging to an upper bound. Using compactifications of free products, two generator compact monoids with these properties are constructed.