关键词: 知识网, 等价关系, 功能拓扑空间, 基, 基本知识点, 约简, 传递闭包

Abstract: Aiming at the rationality of new knowledge mesh， which was obtained from the self-reconfiguration of knowledge-oriented manufacturing systems， the inherent structure principles of the knowledge mesh was studied. Firstly， the sets of the knowledge points were classified by the equivalent relationships， and the function topological space was constructed. Relationships between the sets of the knowledge points and the function topological space were established by the real set. In the function topological space， the base-related conclusions were presented， which indicated the essential mapping relationships of the knowledge mesh， topological space and base. After knowing the principles of mapping relationships， structure of the knowledge mesh was simplified by using the equivalent relationship， the base and the basic knowledge points. Completeness of the complex relationships in the knowledge mesh was studied by the transitive closure. These conclusions could simplify the structure and enhance the rationality of the knowledge mesh. Finally， the given example revealed that these theories were effective.

Key words: knowledge mesh, equivalent relation, function topological space, base, basic knowledge point, reduction, transitive closure