| MTL代数中素滤子集上的拓扑 |
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| 引用本文： | 赵晓东,张家录.MTL代数中素滤子集上的拓扑[J].湘南学院学报,2011,32(2):15-18. |
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| 作者姓名： | 赵晓东 张家录 |
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| 作者单位： | 赵晓东,Zhao Xiaodong(四川民族学院,数学系,四川,康定,626001);张家录,Zhang Jialu(湘南学院,数学系,湖南,郴州,423000) |
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| 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),TIM(M)是紧致的Hausdorff空间.
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| 关 键 词： | MTL代数 素滤子 极大滤子 拓扑 紧空间 Hausdorff 空间 |
Topology on Prime Filter MTL Algebra Set |
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| Zhao Xiaodong,Zhang Jialu.Topology on Prime Filter MTL Algebra Set[J].Journal of Xiangnan University,2011,32(2):15-18. |
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| Authors: | Zhao Xiaodong Zhang Jialu |
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| Institution: | 1.Department of Mathematics,Sichuan University for Nationalities,Kangding 626001,China;2.Department of Mathematics,Xiangnan University,Chenzhou 423000,China) |
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| Abstract: | 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. |
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| Keywords: | MTL algebras prime filter maximal filter topology compact space Hausdorff space |
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