Open AccessSeparability in (strongly) topological gyrogroups
Author(s) -
Meng Bao,
Xiaoyuan Zhang,
Xiaoquan Xu
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2113381b
Subject(s) - separable space , mathematics , metrization theorem , topological manifold , topology (electrical circuits) , topological group , countable set , homeomorphism (graph theory) , pure mathematics , discrete mathematics , combinatorics , topological tensor product , mathematical analysis , functional analysis , biochemistry , chemistry , gene
Separability is one of the most basic and important topological properties. In this paper, the separability in (strongly) topological gyrogroups is studied. It is proved that every first-countable left ?-narrow strongly topological gyrogroup is separable. Furthermore, it is shown that if a feathered strongly topological gyrogroup G is isomorphic to a subgyrogroup of a separable strongly topological gyrogroup, then G is separable. Therefore, if a metrizable strongly topological gyrogroup G is isomorphic to a subgyrogroup of a separable strongly topological gyrogroup, then G is separable, and if a locally compact strongly topological gyrogroup G is isomorphic to a subgyrogroup of a separable strongly topological gyrogroup, then G is separable.