模糊半开集和半分离性公理

Fuzzy Semi—open Sets and Semi—seperation Axioms

本文改进了文[3]的模糊半开集定义,在本文定义的模糊半开集定义,不仅可以完全保留文[3]的结论,而且还能建立分明拓扑空间及其诱导拓扑空间关于半开集、半闭集等对应关系。此外,本文借助重域概念重新定义了半-R_0,半-R_1和半-T_2空间,与[4]相比,本文定义的半分离性公理体系可以更自然地推广分明拓扑空间中的有关定理。

In this paper, the definition of Fuzzy semi—open sets in paper [3] is improved. New defintion not only possessed the whole properties of paper[3], but also can establish the corresponding relations between semi—open sets in General Topology and Fuzzy semi—open sets in its induced Topology. Besides, Fuzzy semi—R, semi—R_1 and semi—T_2 Topological spaces are redefined. It is more convenient to extend the properties about semi—seperation Axioms in General Topology than that in paper[4].