关于Fuzzy拓扑线性空间的某些结果

本文给出了Ｆｕｚｚｙ拓扑线性空间的若干特征刻划，简化了判断Ｆｕｚｚｙ拓扑线性空间的条件，研究了Ｆｕｚｚｙ拓扑线性空间的层次结构，揭示了Ｆｕｚｚｙ拓扑线性空间与分明拓扑线性空间的内在联系，得到了Ｆｕｚｚｙ拓扑线性空间的“平移不变性”与“局部凸性”都是可截性质。     

一类包含S—闭空间和紧空间的拓扑空间

本文定义了WS—闭空间的概念,它是S—闭空间和紧空间的推广.文中讨论了WS—闭空间的一些性质,推广了s—闭空间的一些结果.     

SPECTRAL空间

讨论了spectral空间的基本性质,以及它与Priestley空间的关系,主要结果有:1)若X是spectral空间,其则关于patch拓扑及X上诱导序为Priestley空间;2)若(X,τ,≤)为Priestley空间,则其开上集拓扑空间是spectral的.最后给出spectral空间的谱理论.     

Fuzzy拓扑共生预序空间

文[1]给出了研究拓扑空间,邻近空间,一致空间的统一化理论的方法,提出了拓扑共生结构的概念。文[3,4]引入了Fuzzy拓扑共生结构,初步研究了Fuzzy拓扑,Fuzzy邻近结构,Fuzzy一致结构的统一化问题,文[5]讨论了Fuzzy拓扑共生结构生成     

F连续线性映象空间

本文采用（１）中给出的Ｆｕｚｚｙ拓扑线性空间的定义，并利用Ｆｕｚｚｙ拓扑线性空间的有关理论，对Ｆｕｚｚｙ连续线性映象空间作了较深入的研究。     

关于C—序列空间与Mazur空间的进一步研究

本深入讨论C－序列空间与Mazur空间的性质,对二进行了比较并分别证明了其遗传性。     

函数空间上的模糊线性拓扑

本文给出了模糊拓扑向量空间（Ｘ，Ｗ）到（Ｙ，Ｊ）的函数族Ｆ上的模糊线性拓扑，证明了若值域空间（Ｙ，Ｊ）是（Ｑ）型的、局部凸的模糊拓扑向量空间，则（Ｆ，），也是型的、局部凸的模糊拓扑向量空间。     

概率内积空间

本文给出概率内积空间的新定义,讨论了通常的内积空间与概率内积空间的关系,建立了Schwarz不等式,讨论了概率内积空间与概率赋范空间的关系,建立了概率内积空间上的拓扑,建立了连续性、正交性概念。     

模糊软拓扑空间上的和空间

利用模糊软拓扑空间族,构造出模糊软和拓扑,得到相应的模糊软和拓扑空间的系列拓扑性质。最后给出模糊软Ti-空间族的和空间(i=0,1,2,3,4)的一些结论。     

模糊桶空间

文中给出了模糊桶空间的定义，在此基础上，研究了模糊桶空间的一系列重要定理。     

Toeplitz Operators on Dirichlet Spaces

In this paper we study Toeplitz operators on Dirichlet spaces and describe the boundedness and compactness of Toeplitz operators on Dirichlet spaces. Meanwhile, we give density theorems for Toeplitz operators on Dirichlet spaces Received December 22,1998, Revised March 27, 2000, Accepted June 27, 2000     

Fuzzy Closure Spaces vs. Fuzzy Rough Sets

This paper investigates the relationship among fuzzy rough sets, fuzzy closure spaces and fuzzy topology. It is shown that there exists a bijective correspondence between the set of all fuzzy reflexive approximation spaces and the set of all quasi-discrete fuzzy closure spaces satisfying a certain extra condition. Similar correspondence is also obtained between the set of all fuzzy tolerance approximation spaces and the set of all symmetric quasi-discrete fuzzy closure spaces satisfying a certain extra condition.     

L-fuzzy拓扑空间的层浓度

在Ｌ－ｆｕｚｙ拓扑学中引入了层稠密集、层第一纲集、层Ｂａｉｒｅ空间、层浓度、及层可分空间等概念，研究了它们的基本性质，讨论了它们与分明拓扑学中相应概念的关系．     

关于弱MCP空间与弱层空间

本文引入了与已知的一些空间类非常类似的两个概念,我们分别称它们为弱MCP空间与弱层空间.本文主要讨论了这两空间类的等价命题与一些基本性质,及它们与原有空间类的关系.     

Merotopological Spaces

In this paper we introduce a new topological-type of structured set called merotopological space. The appropriate morphisms are defined and characterizations of the corresponding initial and final structures are given. The resulting category contains as fully embedded subcategories not only the category of topological spaces and continuous maps but also the category of merotopic spaces and uniformly continuous maps, and, a fortiori, the category of nearness spaces and the category of uniform spaces. A functorial completion is constructed for merotopological spaces using bunches. A problem that has remained long open in the setting of nearness spaces is to find an internal characterization of the epireflective hull of the topological spaces. We solve the analogue of this problem in the setting of merotopological spaces. Applications to the Wyler prime closed filter compactification and to Taimanov's extension theorem are given.     

$l^{0}(\{X_{i}\})$型赋$F$-范空间的共轭空间的表示定理

作者在《数学学报》(2016, {\bf 59}(4))上的一篇文章中, 给出了几个$l^{0}$型赋$F$-范空间的共轭空间的表示定理. 对于赋范空间序列$\{X_{i}\}$,本文研究$l^{0}(\{X_{i}\})$型赋$F$- 范空间的共轭空间的表示问题,得到代数表示连等式$\left(l^{0}(\{X_{i}\})\right)^{*}\stackrel{A}{=}\left(c^{0}_{00}(\{X_{i}\})\right)^{*}\stackrel{A}{=}c_{00}(\{X^{*}_{i}\})$,$$\left(l^{0}(X)\right)^{*}\stackrel{\mathrm{A}}{=}\left(c^{0}(X)\right)^{*}\stackrel{\mathrm{A}}{=}\left(c_{0}^{0}(X)\right)^{*}\stackrel{\mathrm{A}}{=}\left(c^{0}_{00}(X)\right)^{*}\stackrel{\mathrm{A}}{=}c_{00}(X^{*}),$$以及序列弱星拓扑下的拓扑表示定理$\left(c^{0}_{00}(\{X^{*}_{i}\}),sw^{*}\right)=c^{0}_{00}(\{X^{*}_{i}\})$. 对于内积空间序列与通常拓扑下的数域空间序列,文章最后给出了基本表示定理的具体表现形式.     

近似空间的拓扑性质及其应用

近似空间(U,R)的全体可定义集构成X上的一个拓扑.本文在不要求论域U是有限的前提下探讨近似空间上这个拓扑的局部性质和可数性质,以及拓扑空间可近似化的充要条件及公理化体系,并寻找它们在粗糙集理论中的应用.     

I-Fuzzy拓扑空间中的基与子基

本文给出了I-fuzzy拓扑空间中基与子基的合理定义,对连续映射和开映射进行了刻画。此外,文中界定了乘积空间中基与子基并研究了乘积空间与因子空间的关系。     

L-模糊化拓扑空间中的Moore-Smith收敛理论

This paper presents a definition of L-fuzzifying nets and the related L-fuzzifying generalized convergence spaces. The Moore-Smith convergence is established in L-fuzzifying topology. It is shown that the category of L-fuzzifying generalized convergence spaces is a cartesianclosed topological category which embeds the category of L-fuzzifying topological spaces as a reflective subcategory.     

On Homeomorphisms of Effective Topological Spaces

We study effective presentations and homeomorphisms of effective topological spaces. By constructing a functor from the category of computable models into the category of effective topological spaces, we show in particular that there exist homeomorphic effective topological spaces admitting no hyperarithmetical homeomorphism between them and there exist effective topological spaces whose autohomeomorphism group has the cardinality of the continuum but whose only hyperarithmetical autohomeomorphism is trivial. It is also shown that if the group of autohomeomorphisms of a hyperarithmetical topological space has cardinality less than 2 then this group is hyperarithmetical. We introduce the notion of strong computable homeomorphism and solve the problem of the number of effective presentations of T ₀-spaces with effective bases of clopen sets with respect to strong homeomorphisms.