On locally compact semitopological graph inverse semigroups

摘要

In this paper we investigate locally compact semitopological graph inversesemigroups. Our main result is the following: if a directed graph $E$ isstrongly connected and contains a finite amount of vertices then a locallycompact semitopological graph inverse semigroup $G(E)$ is either compact ordiscrete. This result generalizes results of Gutik and Bardyla who proved theabove dichotomy for locally compact semitopological polycyclic monoids$\mathcal{P}_1$ and $\mathcal{P}_{\lambda}$, respectively.