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On separation axioms of topological rough groups

  • Foundation, algebraic, and analytical methods in soft computing
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Abstract

In this paper, separation axioms of topological rough groups are discussed. Two examples are constructed to show that there exist Hausdorff topological rough groups such that they have no regular separation. This answers an open question posed in (Lin et al. in Soft Comput 25: 3441-3453, 2020). We also consider regularity of a strongly topological rough group.

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Funding

Supported by Natural Science Foundation of Hebei Province (A2018501040, A2019210318) and Beijing Natural Science Foundation (No. 1212001).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, 221018, China

    Pi-Yu Li

  2. School of Mathematics and Information Science, Anshan Normal University, Anshan, 114056, China

    Wen-Li Liu

  3. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Lei Mou

  4. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Zhi-Fang Guo

Authors
  1. Pi-Yu Li
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  2. Wen-Li Liu
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  3. Lei Mou
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  4. Zhi-Fang Guo
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Contributions

The authors discussed and wrote the paper together. The first three authors contributed equally to the original work and the fourth author contributed to the revision.

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Correspondence to Pi-Yu Li.

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Li, PY., Liu, WL., Mou, L. et al. On separation axioms of topological rough groups. Soft Comput 27, 57–61 (2023). https://doi.org/10.1007/s00500-022-07521-x

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