THE HARTMAN–MYCIELSKI CONSTRUCTION IN TOPOLOGICAL GYROGROUPS

Abstract

The concept of gyrogroups is a generalization of groups that does not explicitly have associativity. Recently, Wattanapan et al. considered the Hartman–Mycielski construction in strongly topological gyrogroups. In this paper, we extend their results in topological gyrogroups. We mainly, among other results, prove that every Hausdorff topological gyrogroup $G$ can be embedded as a closed subgyrogroup of a Hausdorff path-connected and locally path-connected topological gyrogroup $G^{•}$.