对称传递关系的诱导拓扑及其可数性

doi:10.3778/j.issn.1002-8331.1704-0119

计算机工程与应用 ›› 2018, Vol. 54 ›› Issue (11): 35-40.DOI: 10.3778/j.issn.1002-8331.1704-0119

对称传递关系的诱导拓扑及其可数性

孙小义1，2，张贤勇1，2，李露1，2

1.四川师范大学数学与软件科学学院，成都 610066
2.四川师范大学智能信息与量子信息研究所，成都 610066

出版日期:2018-06-01 发布日期:2018-06-14

Induced topology and its countability based on symmetric and transitive relation

SUN Xiaoyi1，2, ZHANG Xianyong1，2, LI Lu1，2

1.College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China
2.Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu 610066, China

Online:2018-06-01 Published:2018-06-14

摘要/Abstract

摘要： 粗糙集通过二元关系密切联系拓扑，并具有基于自反、自反传递、自反对称等关系的拓扑研究。采用对称传递关系构建拓扑并研究其可数性。基于对称传递关系，定义粗糙集近似集，由此建立拓扑及内部、闭包；针对构建拓扑，确立基与邻域基，得到第二可数性、第一可数性、可分性、林德洛夫性等可数性特征；提供实例分析。研究结果基于新二元关系揭示粗糙集与拓扑深入联系。

关键词: 粗糙集, 二元关系, 对称传递关系, 拓扑, 可数性

Abstract: Rough sets depend on binary relations to closely adhere to topologies, and exhibit topology studies based on reflexive, reflexive and transitive, reflexive and symmetric relations. Thus, a symmetric and transitive relation is adopted to construct a topology, and its topological countability is investigated. Based on a symmetric and transitive relation, approximations of rough sets are defined, and the corresponding topology, interior and closure are constructed; according to the induced topology, the base and neighborhood base are established to gain countability including the second coutability and first coutability, separability, and Lindelof feature; example analyses are finally provided. The obtained results resort to the new type of binary relations to reveal in-depth connections between rough sets and topologies.

Key words: rough set, binary relation, symmetric and transitive relation, topology, countability

孙小义1，2，张贤勇1，2，李露1，2. 对称传递关系的诱导拓扑及其可数性[J]. 计算机工程与应用, 2018, 54(11): 35-40.

SUN Xiaoyi1，2, ZHANG Xianyong1，2, LI Lu1，2. Induced topology and its countability based on symmetric and transitive relation[J]. Computer Engineering and Applications, 2018, 54(11): 35-40.

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对称传递关系的诱导拓扑及其可数性

Induced topology and its countability based on symmetric and transitive relation

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