On a complete topological inverse polycyclic monoid

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

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