On a complete topological inverse polycyclic monoid

S. O. Bardyla, O. V. Gutik


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.


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

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