On locally compact semitopological graph inverse semigroups

S. Bardyla
Ivan Franko National University of Lviv, Lviv, Ukraine
In this paper we investigate locally compact semitopological graph inverse semigroups. Our main result is the following: if a directed graph $E$ is strongly connected and has finitely many vertices, then any Hausdorff shift-continuous locally compact topology on the graph inverse semigroup $G(E)$ is either compact or discrete. This result generalizes results of Gutik and Bardyla who proved the above dichotomy for Hausdorff locally compact shift-continuous topologies on polycyclic monoids $\mathcal{P}_1$ and $\mathcal{P}_{\lambda}$, respectively.
locally compact space; semitopological semigroup; polycyclic monoid; graph inverse semigroup
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Matematychni Studii
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