MTL代数中素滤子集上的拓扑  

Topology on Prime Filter MTL Algebra Set

作　　者：赵晓东[1] 张家录[2] 

机构地区：[1]四川民族学院数学系,四川康定626001 [2]湘南学院数学系,湖南郴州423000

出　　处：《湘南学院学报》2011年第2期15-18,共4页Journal of Xiangnan University

摘　　要：通过研究MTL代数M中滤子、极大滤子的性质,在M的全体素滤子集P(M)上引进拓扑T并研究拓扑空间(P(M),T)的紧致性、分离性、连通性等拓扑性质,证明了(P(M),T)是紧致的T0空间.如果把P(M)上拓扑T限制在M的全体极大滤子集M(M)上,则(M(M),T|M(M))是紧致的Hausdorff空间.In this paper,by investigating the properties of M filter and Maximal filter of the MTL algebras,and introducing topology T to the prime filter P(M),we will discuss the topological properties,such as compactness,separation,and connectivity.Also we are to prove that the topological space(P(M),T) is a compactT0space.If the topology T on P(M) was restricted to M set of all maximal filter M(M),then(M(M),T|M(M)) is a compact Hausdorff space.

关 键 词：MTL代数 素滤子 极大滤子 拓扑 紧空间 HAUSDORFF空间 

分 类 号：O189.2[理学—数学]