Separability in (strongly) topological gyrogroups | Zendy

Meng Bao | Zendy; Xiaoyuan Zhang | Zendy; Xiaoquan Xu | Zendy

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Separability 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.

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