拓扑剩余格  

Topology on residuated lattices

作　　者：贺永春 练利锋 He Yongchun;Lian Lifeng(School of Mathematics and Statistics, Yulin University, Yulin 718000, China;School of Mathematics and Information Engineering,Chongqing University of Education, Chongqing 400065, China)

机构地区：[1]榆林学院数学与统计学院,陕西榆林718000 [2]重庆第二师范学院数学与信息工程学院,重庆400065

出　　处：《纯粹数学与应用数学》2017年第5期545-550,共6页Pure and Applied Mathematics

基　　金：陕西省教育厅项目(15JK1859);重庆第二师范学院校项目(KY201548C)

摘　　要：利用剩余格L中滤子系统F={F_i:i∈Λ}诱导的拓扑τ_F,证明了(L,τ_F)是拓扑剩余格,给出拓扑剩余格(L,τ_F)中任意一个非空集合的闭包的表达形式,并且在给定的一些特殊的条件下证明了(L,τ_F)是Hausdorff空间.In this paper,by using a special family of filters on a residuated lattice L,we construct a topology F on L,show that(L;F)is a topological residuated lattice,find the closure of any subsets of L and obtain some conditions under which that(L;F)is a Hausdorff space.

关 键 词：拓扑剩余格 滤子系统 HAUSDORFF空间 

分 类 号：O159[理学—数学]