形式背景的几种分离性

Separations of formal contexts

利用拓扑方法定义了形式背景的T0,T1,T2分离性,探讨几种分离性之间的关系,并研究诸分离性的性质.证明了诸分离性对兼容子背景是遗传的且被满足一定条件的背景映射所保持.另外,还得到拓扑空间(X,τ)的上述几种分离性与形式背景(X,τ,∈)的相应分离性在一定条件下是一致的.

This paper introduces separations T0, T1 and T2 of formal contexts by means of topological methods. Relationships among them are discussed and properties of them are studied. It is proved that separations T0, T1 and T2 of formal contexts are hereditary for compatible sub-contexts and that separations T0, T1 and T2 of formal contexts are preserved by context mappings satisfying certain conditions. Furthermore, it is obtained that for a topological space, its separations mentioned above are equivalent to the corresponding separations of the induced formal context under some suitable conditions.