Classifying locally compact semitopological polycyclic monoids

Abstract

We present a complete classification of Hausdorff locally compact polycyclic monoids up to a topological isomorphism. A {\em polycyclic monoid} is an inverse monoid with zero, generated by a subset $\Lambda$ such that $x{x}^{-1}=1$ for any $x\in \Lambda$ and $x{y}^{-1}=0$ for any distinct $x,y\in \Lambda$. We prove that any non-discrete Hausdorff locally compact topology with continuous shifts on a polycyclic monoid $M$ coincides with the topology of one-point compactification of the discrete space $M\setminus \{0\}$.

Cited by in corpus (3)

• Topological properties of Taimanov semigroups
• On locally compact shift-continuous topologies on the $\alpha$-bicyclic monoid
• On the semigroup ${\text{ID}}_{\infty }$