Some notes on strongly topological gyrogroups

Abstract

A topological gyrogroup is 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 find an error of the proof in [6,Lemma 3.13], then we revise the construction of metric and reprove the result that a strongly topological gyrogroup G is feathered iff it contains a compact L-subgyrogroup P such that the quotient space G/Pis metrizable. Then, combining generalized metric properties, some characterizations of metrizability on quotient spaces of gyrogroups with respect to strong subgyrogroups are researched.

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