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Covering Topology Countability Based on a Subbasis

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Part of the Advances in Intelligent Systems and Computing book series (AISC,volume 646)


Covering topology is induced by covering rough sets, and its topological property is worth researching. In this paper, covering topology countability is studied by a subbasis. At first, basic definitions and properties are achieved for the covering topology countability based on a subbasis, including the first and second countability. Then, the relevant connections between countability and separability are revealed. Finally, three examples are given for illustration. This study establishes subbasis -based countability to deepen covering topology.


  • Rough set
  • Covering topology
  • Countability
  • Subbasis

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  • DOI: 10.1007/978-3-319-66514-6_6
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Thanks to the support by the National Natural Science Foundation of China (No. 61673285, No. 11671284 and No. 61203285), Sichuan Science and Technology Project of China (No. 2017JY0197) and Sichuan Youth Science and Technology Foundation of China (No. 2017JQ0046).

Recommender: Ji-lin Yang, Associate Professor, Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu, 610066, China.

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Correspondence to Xian-yong Zhang .

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Huang, Yc., Mo, Zw., Zhang, Xy. (2018). Covering Topology Countability Based on a Subbasis. In: Cao, BY. (eds) Fuzzy Information and Engineering and Decision. IWDS 2016. Advances in Intelligent Systems and Computing, vol 646. Springer, Cham.

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