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<p>A discrete subset <i>S</i> of a topological gyrogroup <i>G</i> with the identity 0 is said to be a <i>suitable set</i> for <i>G</i> if it generates a dense subgyrogroup of <i>G</i> and <i>S</i> ⋃ {0} is closed in <i>G</i>. In this paper, it is 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.</p>

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Suitable sets for strongly topological gyrogroups

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Fu-cai Lin,
  • Meng Bao,
  • Ting-ting Shi

摘要

A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S ⋃ {0} is closed in G. In this paper, it is 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.