# On locally compact topological graph inverse semigroups

## TL;DR

This paper characterizes which graph inverse semigroups can have only discrete locally compact topologies, providing a complete answer to a question posed by previous researchers in the field.

## Contribution

It offers a full characterization of topological graph inverse semigroups that admit only discrete locally compact topologies, resolving an open problem.

## Key findings

- Identifies conditions for discrete locally compact topologies on graph inverse semigroups
- Provides a complete classification answering prior open questions
- Advances understanding of topological properties of inverse semigroups

## Abstract

In this paper we characterise graph inverse semigroups which admit only discrete locally compact semigroup topology. This characterization provides a complete answer on the question of Z. Mesyan, J. D. Mitchell, M. Morayne and Y. H. P\'eresse posed in their paper "Topological graph inverse semigroups".