On strongly topological gyrogroups

Abstract

A topological gyrogroup, as a generalization of the topological group, is defined as a gyrogroup endowed with a topology such that the binary operation is jointly continuous and the inverse mapping is also continuous. In this paper, we give an example such that a topological group $G$ is a $csf$-countable $k$-space, but $G$ is not sequential, which gives an answer to a question posed by Gabriyelyan, Kakol and Leiderman in [22]. Then it is proved that every feathered $csf$-countable strongly topological gyrogroup is metrizable. Finally, we extend some important results of topological groups to strongly topological gyrogroups.

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