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. 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.

10 pages

References in corpus (4)

• On H-closed paratopological groups
• Semigroup Closures of Finite Rank Symmetric Inverse Semigroups
• $H$-closed quasitopological groups
• Brandt extensions and primitive topological inverse semigroups

Cited by in corpus (5)

• Classifying locally compact semitopological polycyclic monoids
• Completeness and absolute $H$-closedness of topological semilattices
• On locally compact semitopological $0$-bisimple inverse $\omega$-semigroups
• On the lattice of weak topologies on the bicyclic monoid with adjoined zero
• On locally compact shift-continuous topologies on the $\alpha$-bicyclic monoid