# On locally compact semitopological graph inverse semigroups

Author
Ivan Franko National University of Lviv, Lviv, Ukraine
Abstract
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.
Keywords
locally compact space; semitopological semigroup; polycyclic monoid; graph inverse semigroup
DOI
doi:10.15330/ms.49.1.19-28
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Pages
19-28
Volume
49
Issue
1
Year
2018
Journal
Matematychni Studii
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