Separability in (strongly) topological gyrogroups
Abstract
Separability is one of the most basic and important topological properties. In this paper, the separability in (strongly) topological gyrogroups is studied. It is proved that every first-countable left {\omega}-narrow strongly topological gyrogroup is separable. Furthermore, it is shown that if a feathered strongly topological gyrogroup G is isomorphic to a subgyrogroup of a separable strongly topological gyrogroup, then G is separable. Therefore, if a metrizable strongly topological gyrogroup G is isomorphic to a subgyrogroup of a separable strongly topological gyrogroup, then G is separable, and if a locally compact strongly topological gyrogroup G is isomorphic to a subgyrogroup of a separable strongly topological gyrogroup, then G is separable.
Cite
@article{arxiv.2011.02633,
title = {Separability in (strongly) topological gyrogroups},
author = {Meng Bao and Xiaoyuan Zhang and Xiaoquan Xu},
journal= {arXiv preprint arXiv:2011.02633},
year = {2020}
}
Comments
the separability in (strongly) topological gyrogroups is studied and some important and interesting results are obtained. For example, if a feathered strongly topological gyrogroup G is isomorphic to a subgyrogroup of a separable strongly topological gyrogroup, then G is separable