Abstract: The paper presents the topological interpretation of compatibility kernel. Given a compatibility relation R on the universe of discourse, it is pointed out that the topology of interior sets, associated with the quasi-discrete closure space that is induced by binary relation R, is precisely the topology, which has as base the collection of R_ relative set of each element. Also, by exploiting the specification preorder of this topology, it is pointed out that the compatibility kernel of each element is the closure, in the sense of the topology of interior sets, of singleton.

Key words: Compatibility kernel, Quasi-discrete closure space, Topology of interior sets

摘要： 给出了相容核的拓扑解释。给定论域上的一个相容关系R，指出该相容关系诱导的拟离散闭包空间的内集拓扑是以每个元素的R_相关集构成的集族为拓扑基生成的。进而利用该内集拓扑所对应的指定预序，证明了每个元素的相容核就是内集拓扑中单点集的闭包。

关键词: 相容核, 拟离散闭包空间, 内集拓扑

CLC Number: 

• TP18