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高校应用数学学报
高校应用数学学报  2019, Vol. 34 Issue (2): 227-    
    
否定非对合剩余格上基于正规模糊理想的一致拓扑空间
刘春辉
赤峰学院数学与统计学院, 内蒙古赤峰024001
Uniform topological spaces base on normal fuzzy ideals in negative non-involutive residuated lattices
LIU Chun-hui
Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, China
 全文: PDF(276 KB)  
摘要： 拓扑结构是逻辑代数研究领域的重要研究内容之一, 为了揭示否定非对合剩
余格上的拓扑结构, 基于正规模糊理想诱导的同余关系在否定非对合剩余格上构造一
致拓扑空间并讨论其拓扑性质. 证明了: (1) 一致拓扑空间是第一可数, 零维, 非连通,
局部紧的完全正则空间; (2) 一致拓扑空间是T1空间当且仅当是T2空间; (3) 否定非对
合剩余格中格运算和伴随运算关于一致拓扑都是连续的, 从而构成拓扑否定非对合剩
余格. 同时, 获得了一致拓扑空间是紧空间和离散空间的充分必要条件. 最后, 讨论了
拓扑否定非对合剩余格中代数同构与拓扑同胚间的关系. 对从拓扑层面进一步揭示否
定非对合剩余格的内部特征具有一定的促进作用.
关键词： 模糊逻辑代数;  否定非对合剩余格;  正规模糊理想;  一致拓扑空间;  同胚    
Abstract: Topological structure is one of important research contents in the field of logical algebra.
In order to describe the topological structure of negative non-involutive residuated lattices, based
on the congruences induced by normal fuzzy ideals, uniform topological spaces are established and some
of their properties are discussed. The following conclusions are proved: (1) every uniform topological
space is ˉrst-countable, zero-dimensional, disconnected, locally compact and completely regular. (2) a
uniform topological space is a T1 space i? it is a T2 space. (3) the lattice and adjoint operations in a
negative non-involutive residuated lattice are continuous under the uniform topology, which make the
negative non-involutive residuated lattice to be topological negative non-involutive residuated lattice.
Meanwhile, some necessary and sufficient conditions for the uniform topological spaces to be compact
and discrete are obtained. Finally, the relationships between algebraic isomorphism and topological
homeomorphism in topological negative non-involutive residuated lattice are discussed. The results of
this paper have a positive role to reveal internal features of negative non-involutive residuated lattices
on a topological level.
Key words: fuzzy logical algebra    negative non-involutive residuated lattice    normal fuzzy ideal    uniform topological space    homeomorphism
出版日期: 2019-07-05
CLC:  O153.1  
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刘春辉

引用本文:

刘春辉. 否定非对合剩余格上基于正规模糊理想的一致拓扑空间[J]. 高校应用数学学报, 2019, 34(2): 227-.

LIU Chun-hui. Uniform topological spaces base on normal fuzzy ideals in negative non-involutive residuated lattices. Applied Mathematics A Journal of Chinese Universities, 2019, 34(2): 227-.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2019/V34/I2/227

[1] 荣宇音, 徐罗山. 广义近似空间的粗糙同胚与拓扑同胚[J]. 高校应用数学学报, 2017, 32(3): 315-320.
[2] 刘春辉. 否定非对合剩余格的LI-理想理论[J]. 高校应用数学学报, 2015, 30(4): 445-456.