Computer Engineering and Applications ›› 2018, Vol. 54 ›› Issue (18): 52-57.DOI: 10.3778/j.issn.1002-8331.1707-0362

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Strong semi-separation axiom in Fuzzifying topological spaces

YANG Wenhua   

  1. School of Statistics and Mathmatics, Inner Mongolia University of Finance and Economics, Huhhot 010020, China
  • Online:2018-09-15 Published:2018-10-16



  1. 内蒙古财经大学 统计与数学学院,呼和浩特 010020

Abstract: In Fuzzifying topological spaces, using the semantic method of continuous logic, and strong semi-open sets, strong semi-neighborhood, strong semi-interior, strong semi-closure as tools, strong semi-separation axioms [SPT0,][SPT1,][SPT2,][SPT3,][SPT4]are introduced. In addition, equivalent characterizations of them are given, and the relations of each other are discussed. The results show that the separation axioms are not only compatible themselves, but also it can be seen as a useful complement to those have existence.

Key words: Lukasiewicz logic, Fuzzifying topology, strong semi-open sets, strong semi-separationaxiom

摘要: 在[Fuzzifying]拓扑空间中,运用连续值逻辑[LΝ1](赋值格为[Lukasiewicz]单位区间)语义的方法,以强半开集、强半邻域、强半闭包和强半内部等概念为工具引入了[SPT0、][SPT1、][SPT2、][SPT3、][SPT4]强半分离公理,并且给出了五种强半分离公理各自的等价刻画,讨论了它们彼此之间的关系。这套分离公理本身是协调的,可以作为对已有分离公理一种很好的补充。

关键词: Lukasiewicz逻辑, Fuzzifying拓扑, 强半开集, 强半分离性