Suitable sets for strongly topological gyrogroups

Abstract

A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S ∪ {0} is closed in G. In this paper, it was proved that each countable Hausdorff topological gyrogroup has a suitable set; moreover, it is shown that each separable metrizable strongly topological gyrogroup has a suitable set.