m-半格中的滤子及其相关拓扑性质

Filters in m-Semilattices and Their Related Topological Properties

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.