杨忠道定理在L-不分明化拓扑中的推广

将L-不分明化拓扑中的L-不分明化闭包运算的概念扩充到模糊集合上;并把杨忠道定理推广到L-不分明化拓扑中.     

不分明化拓扑中近似紧性和几乎紧性

在不分明化拓扑空间中,从正则开集出发引入了近似紧性和几乎紧性的概念,并且给出了它们的一些性质.这些概念的结合有助于我们对不分明化拓扑的研究。     

基于连续值逻辑上的不分明化拓扑线性空间

在连续逻辑的语义框架下,我们给出了不分明化拓扑线性空间的概念,讨论了零元平衡邻域系的结构和性质,并在不分明化拓扑线性空间中给出不分明化凸集的代数与拓扑性质。     

不分明化拓扑中的SS-紧性

利用连续值逻辑的语义方法将强半开集的概念引入到不分明化拓扑空间中,并由此出发给出了不分明化拓扑空间中SS-紧性,进而讨论了其性质.     

不分明化sp-拓扑空间及范畴FSPTop的拓扑性

基于连续逻辑值语义,研究了不分明化sp-拓扑空间,讨论了不分明化的sp-开集,sp-邻域,sp-闭包及sp-内部等性质,给出了不分明化sp-连续映射的概念,引入了范畴FSPTop,证明了范畴FSPTop是范畴Set上的拓扑范畴。     

不分明化scp-拓扑空间若干性质的研究

本文研究了不分明化scp-拓扑空间中的scp-开集、scp-邻域、scp-闭包以及scp-内部等性质,并给出了不分明化scp-连续映射的概念。     

L-不分明化一致空间和L-不分明化一致拓扑

通过应用完全剩余格值逻辑语义的方法把不分明化一致空间和不分明化一致拓扑推广为L-不分明化一致空间和L-不分明化一致拓扑。并且讨论了L-不分明化一致空间和L-不分明化一致拓扑的一些基本性质。     

概率度量空间中的不分明化拓扑结构

本文引入不分明化 V_D-空间和线性 V_D-空间的概念并以其为工具刻划 PM 空间的拓扑结构和 PN 空间的线性拓扑结构.     

概率度量空间中的不分明化拓扑结构

本文引入不分明化V_D-空间和线性V_D-空间的概念并以其为工具刻划PM空间的拓扑结构和PN空间的线性拓扑结构。     

关于零元L-不分明化邻域基的研究北大核心

本文研究了L-不分明化拓扑线性空间中零元L-不分明化邻域基的相关性质,并证明了满足这些性质的集值映射Bθ可生成一个L-不分明化拓扑线性空间(X,τBθ),而且Bθ恰为其零元L-不分明化邻域基。     

Fuzzifying拓扑中的Pre-网收敛

运用连续值逻辑语义的方法研究fuzzifying拓扑空间,从Pre-开集出发引入了Pre-导集的概念,并且给出了它的一些性质,进一步探讨了Pre-网收敛理论.这些研究有助于丰富和发展fuzzifying拓扑学的基本理论.     

α-Irresoluteness and α-compactness based on continuous valued logic

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying [1]. It investigates topological notions defined by means of α-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by ?ukasiewicz logic in [0, 1]) . The concept of α-irresolute functions and α-compactness in the framework of fuzzifying topology are introduced and some of their properties are obtained. We use the finite intersection property to give a characterization of fuzzifying α-compact spaces. Furthermore, we study the image of fuzzifying α-compact spaces under fuzzifying α-continuity and fuzzifying α-irresolute maps.     

Fuzzifying半拓扑空间的分离公理

在fuzzify ing拓扑空间中,利用fuzzify ing半开集、fuzzify ing半邻域系及fuzzify ing半闭包等概念导入了ST0-,ST1-,ST2-,ST3-,ST4-分离公理,并给出这5个公里的等价命题以及它们的关系。     

Intuitionistic <Emphasis Type="Italic">I</Emphasis>-fuzzy topological spaces

The main purpose of this paper is to introduce the concept of intuitionistic I-fuzzy quasi-coincident neighborhood systems of intuitiostic fuzzy points. The relation between the category of intuitionistic I-fuzzy topological spaces and the category of intuitionistic I-fuzzy quasi-coincident neighborhood spaces are studied. By using fuzzifying topology, the notion of generated intuitionistic I-fuzzy topology is proposed, and the connections among generated intuitionistic I-fuzzy topological spaces, fuzzifying topological spaces and I-fuzzy topological spaces are discussed. Finally, the properties of the operators Iω, ι are obtained.     

KyFan定理在不分明化拓扑中的推广

本文给出了KyFan定理在不分明化拓扑中的推广。     

不分明化拓扑群的一致结构

本文引入了不分明化拓扑群的左、右、双一致结构，讨论了此类一致结构在一致连续下的一些性质，给出了此类结构在其子群上的相对结构和在其乘积上的来积结构。     

Locally α-compact spaces based on continuous valued logic

This paper is a continuation of [1]. That is, it considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying [2]. It investigates topological notions defined by means of α-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Łukasiewicz logic in [0, 1]). Other characterizations of fuzzifying α-compactness are given, including characterizations in terms of nets and α-subbases. Several characterizations of locally α-compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.