  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.
