广义近似空间与拓扑空间

研究了有限论域上的广义近似空间与拓扑空间之间的关系。首先,给出了粗糙隶属函数,拓扑隶属函数的概念。其次,借助粗糙隶属函数刻画了的上下近似算子,借助拓扑隶属函数刻画了的内部闭包算子。再次,利用隶属函数分别从拓扑,二元关系出发构造了关系,拓扑,最终证得拓扑空间与关于自反传递关系的近似空间一一对应。

Generalized Opproximation Spaces and Topology Spaces

This paper is devoted to the discussion of the relationship between generalized opproximation spaces and topology spaces on a finite universe U. Firstly, the notions of rough membership functions and topological membership functions for universe U are introduced. Secondly, it is obtained that rough membership function ηΧ^R and topological membership function μΧ^R can be used to describe approximation operators and interion and closure operators, respectively. Thirdly, based on membership function, Rτ and τR can be constructed from topological τand relation R of universe U , respectively. Finally, it is proved that there exists a one - to - one correspondence between the set of all topological spaces and the set of all approximation spaces in which relation R is reflexitive and transitive.