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
This is a preview of subscription content, access via your institution.
Pawlak, Z.: Rough Sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)
Pomykala, A.J.: Approximation operations in approximation space. Bull. Pol. Acad. Sci. 35(9–11), 653–662 (1987)
Abu-Donia, H.M., Salama, A.S.: Generalization of pawlaks rough approximation spaces by using \(\delta \beta \)-open sets. Int. J. Approx. Reason. 53(7), 1094–1105 (2012)
Zhang, X.Y., Xiong, F., Mo, Z.W.: Covering space and the unification of rough sets and topology. Math. Pract. Theory 36(11), 191–195 (2006). (in Chinese)
Zhang, G.Q.: Topological structures of IVF approximation spaces. Fuzzy Inf. Eng. 8(2), 217–227 (2016)
Salama, A.S.: Topologies controlled by rough sets. Revista Kasmera 43, 87–98 (2015)
Zhang, H., Shu, L., Liao, S.: Topological structures of interval-valued hesitant fuzzy rough set and its application. J. Intell. Fuzzy Syst. 30(2), 1029–1043 (2016)
Skowron, A., Jankowski, A., Swiniarski, R.W.: Foundations of rough sets. In: Janusz, K., Witold, P. (eds.) Springer Handbook of Computational Intelligence, pp. 331–348. Springer, Heidelberg (2015)
Li, Z., Xie, T.: The relationship among soft sets, soft rough sets and topologies. Soft. Comput. 18(4), 717–728 (2014)
El-Bably, M., Embaby, O.A., El-Monsef, M.E., El-Bably, M.K.: Comparison between rough set approximations based on different topologies. Int. J. Granular Comput. Rough Sets Intell. Syst. 3(4), 292–305 (2014)
Abotabl, E.S.A.: On links between rough sets and digital topology. Appl. Math. 05(6), 941–948 (2014)
You, C.Y.: Fundamentals of Topology. Peking University Press, Beijing (1997). (in Chinese)
Qin, B., Xia, G., Yan, K.: Similarity of binary relations based on rough set theory and topology: an application for topological structures of matroids. Soft Comput. 20, 853–861 (2016)
Li, J.J.: Rough sets and subsets of a topological space. Syst. Eng. Theory Pract. 25(7), 136–140 (2005). (in Chinese)
Liu, D.J.: The separateness relative to a subbasis for the topology. Coll. Math. 27(3), 59–65 (2011). (in Chinese)
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.
Editors and Affiliations
Rights and permissions
© 2018 Springer International Publishing AG
About this paper
Cite this paper
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. https://doi.org/10.1007/978-3-319-66514-6_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66513-9
Online ISBN: 978-3-319-66514-6
eBook Packages: EngineeringEngineering (R0)