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蕴涵格及其Fuzzy拓扑表现定理
引用本文:王国俊.蕴涵格及其Fuzzy拓扑表现定理[J].数学学报,1999,42(1):133-140.
作者姓名:王国俊
作者单位:陕西师范大学数学研究所,西安,710062
基金项目:国家自然科学基金!19331030
摘    要:以L-Lindenbaum代数为背景,引入了蕴涵格与正则蕴涵格的概念,讨论了其基本性质,引入了Fuzzy蕴涵空间的概念,为点集拓扑学中零维空间概念的推广.建立了正则蕴涵格的Fuzzy蕴涵空间表现定理,以此为基础可以给出著名的Stone表现定理的另一种证明.

关 键 词:R_0-语义Lindenbaum代数  蕴涵格  正则蕴涵格  Fuzzy蕴涵空间  表现定理  超滤
修稿时间::1997-09-2

Implication Lattices and Their Fuzzy Implication Space Representation Theorem
Wang Guojun.Implication Lattices and Their Fuzzy Implication Space Representation Theorem[J].Acta Mathematica Sinica,1999,42(1):133-140.
Authors:Wang Guojun
Institution:Wang Guojun; (Institute of Mathematics, Shaanxi NormalUniversity, Xi'an 710062, P. R. China); (Email: gjwang@snnu.edu.cn)
Abstract:Taking the concept of L*-Lindenbaum algebra as background, this paper introduced the concepts of implication lattice and regular implication lattice and discussed their basic properties. On the other hand, this paper introduced the concept of fuzzy implication space that is generallization of the concept of zero-dimensional space in point set topology. The representation theorem of regular implication lattices by means of fuzzy implication spaces had been established, that can be seen as, in certain sense, a generalization of the famous Stone’s representation theorem.
Keywords:R_0-semantic Lindenbaum algebra  Implication lattice  Regular Implication lattice  Fuzzy implication space  Representation theorem  Ultra-filter
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