On a complete topological inverse polycyclic monoid

TL;DR

This paper investigates conditions for topological inverse polycyclic monoids to be absolutely H-closed and constructs specific topologies, including an example of a dense embedding of P_2 in a larger inverse monoid.

Contribution

It provides sufficient conditions for absolute H-closure and introduces a coarsest inverse topology on P_λ, along with an example of dense embedding of P_2.

Findings

Conditions for absolute H-closure of P_λ

Construction of the coarsest inverse topology τ_{mi}

Example of P_2 densely embedded in a larger inverse 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. Also, 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.