LF拓扑空间中加强的EsTi(i=1,2,3,4)与EsT31/2分离性

摘要

为进一步研究LF拓扑空间中的分离性,在LF拓扑空间中通过(A) x∈X,P(x)=1或Q(x)=1成立(其中P和Q是更一般的Es远域)和更一般的LF点xλ这两个方面加强EsTi(i=1,2,3,4)的分离性,从而定义加强的EsTi(i =1,2,3,4)分离性;对于定义完全Es正则空间,则借助Es连续的L值Zadeh型函数,进而给出EsT31/2分离性.在加强的EsTi(i=1,2,3,4)与EsT31/2分离性中,分别讨论了其基本性质(即:L-好的推广,弱Es同胚不变性,遗传性,可乘性),并得出CEsT31/2是具有积与上积的范畴.%In LF topological spaces,Es Ti (i =1,2,3,4) separations can actually be strengthened through the setting up of P(x)=1 or Q(x)=1 for (A)x∈X (P and Q hereto are both more common E s remote neighborhoods) and more common LF point x λ,then the notions of strong Es Ti (i =1,2,3,4) separations are defined,so as to further study the separations in LF topological spaces.With Lvalued Zadeh functions of Es continuity,Es-completely regular spaces can be defined,and Es T31/2 separations are then introduced.In addition,in strong Es Ti (i =1,2,3,4) separations and Es T31/2 separations,some of their basic properties (such as L-good generalizations,weak Es homeomorphic invariant property,heritability and productivity) are respectively discussed.Alongside that,it can also be concluded that CEs T31/2 belongs to the category with product and coproduct.