Embedding of locally compact Hausdorff topological gyrogroups in topological groups

Abstract

© 2020 Elsevier B.V. A topological gyrogroup is a topological space endowed with a compatible nonassociative operation, which shares several common properties with topological groups. In this article, we prove that every locally compact Hausdorff topological gyrogroup G can be embedded in a completely regular topological group Γ as a twisted subset. We also study properties shared by them by proving that G has property [Formula presented] if and only if Γ has property [Formula presented], where [Formula presented] is one of the following properties: connectedness, path connectedness, and separability.