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arXiv · 2011.02633

Separability in (strongly) topological gyrogroups

Meng Bao·Xiaoyuan Zhang·Xiaoquan Xu
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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.

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Meng Bao, Xiaoyuan Zhang, Xiaoquan Xu. 2020-11-05. Separability in (strongly) topological gyrogroups. https://arxiv.org/abs/2011.02633

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