The first-countability in the quotient spaces of topological gyrogroups

摘要

In this note, we will prove that if H is a closed strong subgyrogroup of a strongly topological gyrogroup G and H is neutral, then (1) G/H is completely regular; (2) G/H is metrizable if and only if it is first-countable; (3) G/H is submetrizable if and only if it has countable pseudocharacter; (4) G/H is metrizable if and only if it is a bisequential space. In addition, if H is a compact L-subgyrogroup of a topological gyrogroup G, then each compact subspace of G/H is first-countable if and only if every compact subspace of G/H is metrizable. (c) 2023 Elsevier B.V. All rights reserved.