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

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