知识论域,知识拓扑与映射的性质

Knowledge Universe,Knowledge Tology and Topological Properties of Map

定义了知识论域和知识拓扑,组建了4种拓扑空间,并分析了它们之间的联系,为介绍拓扑与映射的联系做了铺垫;讨论了Z.PAWLAK粗糙集模型上映射的拓扑性质,指出了粗糙集模型与一个有限集之间的映射。可以诱导出在此有限集上的等价关系,从而得到了两个粗集拓扑空间的映射。这个映射是连续的,如果是双射则此映射是开的且把粗集映成粗集,粗集的原像还是粗集。本文研究了Z.PAWLAK粗糙集模型上的映射的性质和映射的关系,具有一定的理论价值,从而为使用拓扑学的方法来研究粗糙集的理论成为了可能。

In this Paper, Knowledge universe and knowledge topology are defined. Four kind of topology space are constracted. The connections among and the properties of them are studied. Topological properties of map on Pawlak rough sets model are discussed. And a map between rough set model and a finete set can induce a equivalent relation on the finite set, If the map is regarded as a map between two topological space , then it is continuous . Fourthermore , if the map is bijective , then it is simultaneously open and continuous , the image and inverse image of a rough set are rough.