诱导的L-双拓扑空间的相对配分离性

Relative pairwise separation in induced L-bitopological spaces

将相对分离性引入L-双拓扑空间,研究诱导的L-双拓扑空间的相对配分离性。根据相对拓扑、分子远域等概念,采用分析和归纳的方法,在诱导的L-双拓扑空间中分别定义三类相对配分离性,即相对弱配T-1、T 0、次T 0分离性,相对配T-1、T 0、次T 0分离性,以及相对强配T 0、次T 0分离性等。得出了相对配T 0空间、相对配次T 0空间的等价判断条件,讨论了分明拓扑空间的相对弱T 0(T-1、次T 0)分离性与其拓扑生成的L-双拓扑空间相对弱配T 0(T-1、次T 0)分离性之间的关系,证明了相对配T 0(T-1、次T 0)分离性是L-好的推广。该研究对在L-双拓扑空间开展相关研究具有一定的参考。

This paper introduces a research into the relative pairwise separation of the L-bitopological space by introducing the relative separation into the L-bitopological space.The study building on the relative topology and neighborhood and using the analytical and inductive methods involves developing the three definitions of the relative pairwise separation in induced L-bitopological space,such as relative weakly pairwise T i(i=-1,0)and secondary T 0 separation,relative pairwise T i(i=-1,0)and secondary T 0 separation,relative strong pairwise T 0 separation axioms and secondary T 0 separation;identifying the equivalent conditions of relative pairwise T 0 space and secondary T 0 space;investigating the relationship between the relative weakly-pairwise T i(i=-1,0)and secondary T 0 separation in bitopological space and these in induced L-bitopogical space;and ultimately proving the relative pairwise T i(i=-1,0)and secondary T 0 separation are proved L-Good extension.The research could provide a certain reference for the study in L-bitopological space.