m-半格中的滤子及其相关拓扑性质  

Filters in m-Semilattices and Their Related Topological Properties

作　　者：苏子祺 赵彬[1] SU Ziqi;ZHAO Bin(School of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710119,China)

机构地区：[1]陕西师范大学数学与统计学院,西安710119

出　　处：《吉林大学学报（理学版）》2022年第3期568-576,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11531009).

摘　　要：首先,通过在m-半格中引入滤子的概念,讨论m-半格中滤子的若干性质,进而构造m-半格上的滤子拓扑,得到了滤子空间的一系列性质;其次,证明每个滤子空间是连通的,且双侧m-半格上的滤子空间满足第一可数性公理,并分别给出其为T_(0)空间及满足第二可数性公理的充要条件;最后,通过引入m-半格中素滤子的概念,讨论m-半格上的对偶素谱空间,证明双侧m-半格上的对偶素谱空间是T_(0)空间,并给出其为T_(1)空间的等价刻画.Firstly,by introducing the concept of filters in m-semilattices,some properties of filters in m-semilattices were discussed,then the filter topology on m-semilattices was constructed,and a series of properties of filter spaces were obtained.Secondly,we proved that each filter space was connected,and the filter spaces on two-sided m-semilattices satisfied the first countability axiom.The necessary and sufficient conditions for them to be T_(0) spaces and satisfied the second countability axiom were given respectively.Finally,by introducing the concept of prime filters in m-semilattices,we discussed the dual prime spectral spaces on m-semilattices,proved that the dual prime spectral spaces on two-sided m-semilattices were T_(0) space,and gave its equivalent characterization as T_(1) space.

关 键 词：m-半格 滤子 素滤子 拓扑 对偶素谱 

分 类 号：O153.1[理学—数学]