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Suitable sets for strongly topological gyrogroups

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arxiv 2005.13767 v1 pith:LETUY7QJ submitted 2020-05-28 math.GR math.GN

Fucai Lin , Tingting Shi , Meng Bao This is my paper · ORCID
classification math.GRmath.GN
keywords suitabletopologicalgyrogroupstronglyclosedcountabledensediscrete
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abstract

A discrete subset $S$ of a topological gyrogroup $G$ with the identity $0$ is said to be a {\it suitable set} for $G$ if it generates a dense subgyrogroup of $G$ and $S\cup \{0\}$ 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.

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  1. Strongly topologically orderable gyrogroups with a suitable set

    math.GN 2025-07 conditional novelty 4.0 of 10

    Locally compact and non-totally-disconnected strongly topologically orderable gyrogroups are shown to be metrizable and to contain a suitable set, a discrete generator set that is closed together with the identity.

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