拓扑空间范畴,拓扑FUZZ范畴与拓扑分子格范略畴间的反射与余反射

从整体角度出发，证明拓扑空间范畴Ｔｏｐ分别是拓扑Ｆｕｚｚ范畴ＴｏｐＦｕｚｚ与拓扑分子格范畴ＴＭＬ的反射与余反射满子范畴，ＴｏｐＦｕｚｚｙ是ＴＭＬ的反射与余反射（非满）子范畴。     

拓扑空间范畴、拓扑FUZZ范畴与拓扑分子格范畴间的反射与余反射

从整体角度出发，证明了拓扑空间范畴Ｔｏｐ分别是拓扑Ｆｕｚｚ范畴ＴｏｐＦｕｚ与拓扑分子格范畴ＴＭＬ的反射与余反射满子范畴，ＴｏｐＦｕｚ是ＴＭＬ的反射与余反射（非满）子范畴．     

点式拟一致分子格中的拓扑

分子格Ｌ上的一个点式拟一致结构可以诱导出Ｌ上的一个拓扑和一个余拓扑（）。本文证明了下面结论：（１）在拓扑分子格（Ｌ，＊（））中，每个分子皆有一个由（）一开元组成的远域基；（２）在拓扑空间（Ｌ，（））（这里Ｌ是Ｆｕｚｚｙ格）中，每个分子皆有一个由（）一开元组成的＊远域基；（３）若（Ｌ，）是点式一致Ｆｕｚｚｙ格，则（）＝（）。     

完备格上的上拓扑和区间拓扑

对完备格 Ｌ;记ｖ（Ｌ）为 Ｌ上的上拓扑之闭集格本文证明了完备格 Ｌ为 Ｆ－分配格当且仅当映射ｓｕｐ：ｖ（Ｌ）→Ｌ为满完备格同态;若Ｌ为Ｆ－分配的Ｂｏｏｌｅ格,则Ｌ同构于某幂集格、对Ｔ１格 Ｌ,证明了下述各条件等价。（１） Ｌ同构于某幂集格;（２） Ｌ上的区间拓扑是 Ｈａｕｓｄｏｒｆｆ的;（３）是有限分离的;（４） Ｌ是连续的对马空间（Ｘ,Ｏ（Ｘ））,进一步证明了 Ｏ（Ｘ）上的区间拓扑不可能为 Ｈａｕｓｄｏｒｆｆ的,除非（Ｘ, Ｏ（Ｘ））是离散空间．     

L—fuzzy拓扑空间中的近似良紧性

本文系统地研究了Ｌ－ｆｕｚｚｙ拓扑空间中近奶紧性的特征及其拓扑性质。讨论了近似良紧性与良紧性之间的关系。证明了近似良紧性是正则闭遗传的，有限可和的以及在满层的Ｌ－ｆｕｚｚｙ拓扑空间中，对于近似良紧性而言，ＴΝＸＯＨＯＢ乘积定理成立等重要性质。     

TML中元的明聚点和ST-1分离性

在拓扑分子格（ＴＭＬ）中引进元的明聚点概念，并讨论了聚点的性质，研究了ＳＴ_-1分离性和ＴＭＬ的明导算子．     

完全分配格的谱论与拓扑分子格

本文借助于完全分配格的谱理论是首先证明分子格范畴同构于某连续偏序集范畴子范畴,然后利用上述同构,证明分子格上余拓扑同构于其中分子之集上。与分子序密切相关的某分明拓扑,从而就给“重域”“远域”这两个基本概念以合理解释,并证明许多拓扑分子格性质的研究可以化为相应的拓扑空间性质的研究.“重域”概念的引入,使 fuzzy 拓扑学的研究发生了根本变化,导致了有点派的兴起。而“远域”的引入,则导致因更广的拓扑分子格理论的产生,从而把 Fuzzy 拓扑为学纳入了拓扑格的范畴.本文中我们首先建立分子格范畴与连续偏序集范畴某子范畴的同构,从而把二者的研究紧密结合起来,然后借助上述同构把拓扑分子格中的问题的研究化为连续偏序集中问题去考虑,通过这种转化,我们将会看到,“重域”,“远域”等基本概念确为 fuzzy 拓扑学,拓扑分子格中唯一合理的点与集合的邻属关系,而择一原理这条fuzzy 拓扑学中的基本原理成立的原因也就变得很清楚。本文中凡未定义的概念请参看[4].     

赋层拓扑分子格及其紧性

拓扑分子格本身没有层次结构，为其构造某种层次成为很重要的问题。本文的构思是赋于分子格上的拓扑一种层次，从而使拓扑分子格具有丰富的层次性，其次讨论了保层次序同态与赋层积拓扑分子格，在此基础上建立了较理想的拓扑分子格的紧性。     

拓扑分子格范畴中的积运算

文[1,2]以近年来发展起来的Fuzzy拓扑学中的工作为基础,建立了完全分配格上的点式拓扑理论。在文[1—3]的基础上,文[4]证明了分子格范畴对乘积运算封闭,并给出了其具体构造。本文进一步证明拓扑分子格范畴也对乘积运算封闭,同时给出了拓扑分子格范畴中的乘积结构。本文还证明这种乘积具有良好的性质,比如:连通性是可乘的最后,给出了这种乘积与L-Fuzzy拓扑空间乘积的关系。     

内射拓扑分子格

本文证明了任给T_O拓扑分子格(L,η),以下三条等价:(1)(L,η)为正则内射拓扑分子格;(2)L为完备集环且其完备余素元集ht(L)形成一连续格,余拓扑η为该连续格ht(L)上的Scott闭集格;(3)存在T_O内射拓扑空间(X,Τ),(L,η)同胚于(P(X),Τ~c)在拓扑分子格范畴中的Sober化。此外,还给出了正则内射拓扑分子格、(一般)内射拓扑分子格以及正则内射分子格的一般结构。作为应用,重新证明了有指数元的拓扑分子格的结构。     

Hausdorff properties of topological algebras

Let P be a property of topological spaces. Let [P] be the class of all varieties having the property that any topological algebra in has underlying space satisfying property P. We show that if P is preserved by finite products, and if is preserved by ultraproducts, then [P] is a class of varieties that is definable by a Maltsev condition.?The property that all T ₀ topological algebras in are j-step Hausdor. (Hj) is preserved by finite products, and its negation is preserved by ultraproducts. We partially characterize the Maltsev condition associated to by showing that this topological implication holds in every (2j + 1)-permutable variety, but not in every (2j + 2)-permutable variety.?Finally, we show that the topological implication holds in every k-permutable, congruence modular variety. Received March 1, 2000; accepted in final form October 18, 2001.     

Finite images and characters of topological groups

We investigate conditions under which every finite homomorphic image of a topological group is obtained as that of a continuous homomorphism. An Abelian topological group has such property if it is compact or if it has bounded exponent and sufficiently many characters.     

On Finite Model Property for Admissible Rules

Our investigation is concerned with the finite model property (fmp) with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 itself, S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp–the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width ≤ 2, there exists a zone for fmp w. r. t. admissibility. It is shown (Theorem 4.3) that all modal logics A of width ≤ 2 extending S4 which are not sub-logics of three special tabular logics (which is equipotent to all these λ extend a certain subframe logic defined over S4 by omission of four special frames) have fmp w.r.t. admissibility.     

L—层次拓扑空间的有限覆盖性质

在L—层次拓扑空间中,引入了有限Ir—覆盖性质,并讨论了它的特性.证明了它是闭遗传的,它是在Ir—序同态下保持不变的等性质.     

弱s-置换性传递的有限群

群G被称为弱s-置换性传递的群,对于它的子群H和K,若H在K中弱s-置换,K在G中弱s-置换,则H在G中弱s-置换.本文给出弱s-置换性、弱s-补性传递的可解群的结构以及每一子群在G中弱s-置换、弱s-补的群的结构.     

Self-similar sets satisfying the common point property

A self-similar set is a fixed point of iterated function system (IFS) whose maps are similarities. We say that a self-similar set satisfies the common point property if the intersection of images of the attractor under the maps of the IFS is a singleton and this point has a common pre-image, under the maps of the IFS, and the pre-image is in the attractor.Self-similar sets satisfying the common point property were introduced in Sirvent (2008) in the context of space-filling curves. In the present article we study some basic topological and dynamical properties of self-similar sets satisfying the common point property. We show examples of this family of sets.We consider attractors of a sub-IFS, an IFS formed from the original IFS by removing some maps. We put conditions on this attractors for having the common point property, when the original IFS have this property.     

德摩根拓扑代数上的紧性与q—收敛性

在文（１），（２），（３）的基础上，我们首先在德摩根拓扑代数上用有限覆盖性质定义了紧性，并引入ω－元，ω－ｄ－ｑ－聚点等概念，并着重讨论了紧性与ｑ－收敛性之间的关系。     

Weighted mean topological dimension

This paper is devoted to the investigation of weighted mean topological dimension in dynamical systems. We show that the weighted mean dimension is not larger than the weighted metric mean dimension, which generalizes the classical result of Lindenstrauss and Weiss [16]. We also establish the relationship between the weighted mean dimension and the weighted topological entropy of dynamical systems, which indicates that each system with finite weighted topological entropy or small boundary property has zero weighted mean dimension.     

Modeling Ergodic, Measure Preserving Actionson Shifts of Finite Type

 In this paper we show that shifts of finite type satisfying a strong topological mixing property are universal models for ergodic measure preserving dynamical systems.     

拓扑分子格的PS-T*分离公理

利用准半开邻域引入了拓扑分子格的一类新的PS-Ti*分离公理(i=0,1,2,3,4),给出了这些分离性的刻画,得到了这些分离性是PS-同胚序同态下保持不变的性质。