Locally compact and non-totally-disconnected strongly topologically orderable gyrogroups are shown to be metrizable and to contain a suitable set, a discrete generator set that is closed together with the identity.
Atiponrat, Topological gyrogroups: generalization of topological groups, Topol
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Strongly topologically orderable gyrogroups with a suitable set
Locally compact and non-totally-disconnected strongly topologically orderable gyrogroups are shown to be metrizable and to contain a suitable set, a discrete generator set that is closed together with the identity.