Fuzzy蕴涵代数的素MP-滤子空间

数学季刊 ›› 2012, Vol. 27 ›› Issue (2): 246-253.

Fuzzy蕴涵代数的素MP-滤子空间

1. Department of Elementary Education, Chifeng University 2. Department of Mathematics Science, Yangzhou University

收稿日期:2010-09-09 出版日期:2012-06-30 发布日期:2023-03-29
作者简介:LIU Chun-hui(1982-), male, native of Chifeng, Inner Mongolia, a lecturer of Chifeng University, M.S.D., engages in Domain theory, non-classical mathematical logic and topology; XU Luo-shan(1957-), male, native of Yangzhou, Jiangsu, a professor of Yangzhou University, Ph.D., engages in Domain theory, non-classical logic and topology.
基金资助:
Supported by the NSF of China(10371106,60774073)

Prime MP-ﬁlter Spaces of Fuzzy Implication Algebras

1. Department of Elementary Education, Chifeng University 2. Department of Mathematics Science, Yangzhou University

Received:2010-09-09 Online:2012-06-30 Published:2023-03-29
About author:LIU Chun-hui(1982-), male, native of Chifeng, Inner Mongolia, a lecturer of Chifeng University, M.S.D., engages in Domain theory, non-classical mathematical logic and topology; XU Luo-shan(1957-), male, native of Yangzhou, Jiangsu, a professor of Yangzhou University, Ph.D., engages in Domain theory, non-classical logic and topology.
Supported by:
Supported by the NSF of China(10371106,60774073)

摘要/Abstract

摘要： In this paper, the topological space (PFMP(X), T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T₀-space if X with condition (P). Secondly, we restricted T to the set of all maximal MP-filters MFMP(X) of X and concluded that (PFMP(X), T |(PFMP(X))) is a compact T₂ space if X with conditions (P) and (S).

关键词: Fuzzy implication algebra, MP-filter, prime MP-filter, topological space

Abstract: In this paper, the topological space (PFMP(X), T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T₀-space if X with condition (P). Secondly, we restricted T to the set of all maximal MP-filters MFMP(X) of X and concluded that (PFMP(X), T |(PFMP(X))) is a compact T₂space if X with conditions (P) and (S).

Key words: Fuzzy implication algebra, MP-filter, prime MP-filter, topological space

中图分类号:

O153

刘春辉, 徐罗山. Fuzzy蕴涵代数的素MP-滤子空间[J]. 数学季刊, 2012, 27(2): 246-253.

LIU Chun-hui, XU Luo-shan. Prime MP-ﬁlter Spaces of Fuzzy Implication Algebras[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(2): 246-253.