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arXiv · 2304.07231

On the continuity of the inverse in (strongly) paratopological gyrogroups

Ying-Ying Jin·Li-Hong Xie
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Abstract

In this paper, we consider the continuity of the inverse in (strongly) paratopological gyrogroups. The conclusions are established as follows: (1) A compact Hausdorff paratopological gyrogroup $G$ is a topological gyrogroup. (2) A Hausdorff locally compact strongly paratopological gyrogroup is a topological gyrogroup. (3) If $G$ is locally compact strongly paratopological gyrocommutative gyrogroup (without any separation restrictions), then $G$ is a strongly topological gyrogroup. (4) Every regular feebly compact strongly paratopological gyrogroup is a topological gyrogroup. (5) If a Hausdorff strongly paratopological gyrogroup $G$ is countablly compact and topologically periodic, then $G$ is a strongly topological gyrogroup.

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Ying-Ying Jin, Li-Hong Xie. 2023-03-16. On the continuity of the inverse in (strongly) paratopological gyrogroups. https://arxiv.org/abs/2304.07231

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