On a complete topological inverse polycyclic monoid

Abstract

We give sufficient conditions when a topological inverse $\lambda$-polycyclic monoid $P_{\lambda}$ is absolutely $H$-closed in the class of topological inverse semigroups. For every infinite cardinal $\lambda$ we construct the coarsest semigroup inverse topology $\tau_{mi}$ on $P_\lambda$ and give an example of a topological inverse monoid $S$ which contains the polycyclic monoid $P_2$ as a dense discrete subsemigroup.

Keywords

• inverse semigroup
• bicyclic monoid
• polycyclic monoid
• free monoid
• semigroup of matrix units
• topological semigroup
• topological inverse semigroup
• minimal topology