可数良紧集的刻画与性质

本文借助于α-序列,α-局部有限族及α∧--w聚点等概念给出了可数良紧集的一些等价刻画,进而讨论了可数良紧集在L值Zadeh型函数下的逆不变性,证明了可数良紧集与良紧集的乘只是可数良紧的。     

可数强F紧集的刻画与性质

借助α-ω聚点与α-聚点概念给出可数强F紧集的两个刻画定理,进而讨论可数强F紧集在L值Zadeh型函数下的逆不变性,证明了可数强F紧集与强F紧集的乘积是可数强F紧的。     

Fuzzy序列紧性,可数Fuzzy紧性和Fuzzy列紧性

本文引进了Fuzzy序列紧性、可数Fuzzy紧性和Fuzzy列紧性,它们是一般拓扑学中相应概念的“良扩张”(R. Lowen意义下),文中讨论了这些fts的主要性质,以及它们之间的联系。     

L—Fuzzy拓扑空间中的可数F紧性与几乎可数F紧性

本文在Ｌ－ｕｚｚｙ拓扑空间中引入可数Ｆ紧性与几乎可数Ｆ紧性的概念，并讨论了它们的性质及其相互关系。     

Lukasiewicz语义集上的紧Hausdorff拓扑

以Ω记从全体命题之集F（S）到单位区间的全体Lukasiewicz赋值之集.本文通过一种自然的方法在Ω上引入了Fuzzy拓扑δ,证明了其为第二可数的零维良紧空间,并证明了δ在Ω上生成的截拓扑空间是第二可数的紧Hausdorff空间,从而是可度量化的空间.     

超序列紧fts,可数超紧fts和超列紧fts

文献[1]中定义了序列紧fts(每个不分明集序列有收敛的子序列)和可数紧fts(每个可数开覆盖存在有限子覆盖)。对于序列紧fts,得到“每个fts都是序列紧的”病态结果,由此可见这样定义的序列紧fts不是一般拓扑学中序列紧的良扩张。对于可数紧fts,[2]在评论F-紧性时,论证了凡T_1空间都不是F-紧空间,以上的论证也可得到凡T_1空间都不是可数紧fts的病态结果。我们还要指出,[1]定义的可数紧fts也不是一般拓扑学中可数紧的良扩张。     

关于可数个空间的箱拓扑

讨论了可数个空间的箱拓扑为紧性，序列式紧性，第二可数性，第一可数性，分性及连通性的条件。     

Eberlein mulian定理在局部凸空间中的推广

设（Ｅ，Ｔ）是一个分离的局部凸空间．本文主要结果是：（１）如果（Ｅ，Ｔ）是次可分的，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．（２）如果（Ｅ，Ｔ）是强次可分且（Ｅ，β（Ｅ，Ｅ））是桶型空间，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．     

p-仿紧空间

本文研究了p-仿紧空间和p-可数仿紧空间的相关问题.利用预开集和覆盖性质理论,得到了p-仿紧空间和p-可数仿紧空间的定义、等价刻画及αp-仿紧子集的性质,推广了一般拓扑学中仿紧空间的部分结果.     

L-拓扑空间的局部Fuzzy紧性

定义了L-拓扑空间的局部Fuzzy紧性, 证明了这种局部Fuzzy紧性是L-好的推广, 是闭可遗传的, 在连续的、开的、满的L值Zadeh型函数下保持不变.     

关于模糊数空间的Skorokhod拓扑的注记

首先考察模糊数空间中Skorokhod度量与紧承下方图度量之间的关系,然后说明了文献[4]中的关于Skorokhod拓扑紧致性的例子是错误的并给出了正确的例子.     

A New Form of Fuzzy Compact Spaces and Related Topics via Fuzzy Idealization

Fuzzy ideals and the notion of fuzzy local function were introduced and studied by Sarkar[12] and by Mahmoud in [9]. The purpose of this paper deals with a fuzzy compactness modulo a fuzzy ideal. Many new sorts of weak and strong fuzzy compactness have been introduced to fuzzy topological spaces in the last twenty years but not have been studied using fuzzy ideals so,the main aim of our work in this paper is to define and study some new various types of fuzzy compactness with respect to fuzzy ideals namely fuzzy L-compact and L*-compact spaces. Also fuzzy compactness with respect to ideal is useful as unification and generalization of several others widely studied concepts. Possible application to superstrings and E∞ space-time are touched upon.     

L-Smooth紧

在模糊格上讨论Smooth拓扑空间的Smooth紧性,它定位于每一个模糊集,并兼顾整个Smooth拓扑空间。     

Strong Minkowski Separation and Co-Drop Property

In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski separation are deduced. Using the results, we prove a drop theorem involving weakly countably compact sets in locally convex spaces. Moreover, we introduce the notion of the co-drop property and show that every weakly countably compact set has the co-drop property. If the underlying locally convex space is quasi-complete, then a bounded weakly closed set has the co-drop property if and only if it is weakly countably compact.     

A generalization of Krasnoselskii’s eigenvalue theorem

We give a generalization of Krasnoselskii’s eigenvalue theorem to countably condensing set-valued maps in Banach spaces, where the method is to use a fixed point theorem for compact maps. This is based on the fact that there is a compact fundamental set for a countably condensing map.     

Fuzzy dynamical systems

A fuzzy dynamical system on an underlying complete, locally compact metric state space X is defined axiomatically in terms of a fuzzy attainability set mapping on X. This definition includes as special cases crisp single and multivalued dynamical systems on X. It is shown that the support of such a fuzzy dynamical system on X is a crisp multivalued dynamical system on X, and that such a fuzzy dynamical system can be considered as a crisp dynamical system on a state space of nonempty compact fuzzy subsets of X. In addition fuzzy trajectories are defined, their existence established and various properties investigated.     

Square of countably compact groups without non-trivial convergent sequences

We show in ZFC that the existence of a countably compact Abelian group without non-trivial convergent sequences implies the existence of a countably compact group whose square is not countably compact.This improves a result obtained by van Douwen in 1980: the existence of a countably compact Boolean group without non-trivial convergent sequences implies the existence of two countably compact groups whose product is not countably compact in ZFC.Hart and van Mill showed in 1991 the existence of a countably compact group whose square is not countably compact under Martin's Axiom for countable posets. We show that the existence of such an example does not depend on some form of Martin's Axiom.     

Almost compactness in fuzzy topological spaces

We introduce and study almost compactness for fuzzy topological spaces. We show that the almost continuous image of an almost compact fuzzy topological space is almost compact. Moreover, we show that generally almost compactness for fuzzy topological spaces is not product-invariant, but if X and Y are almost fuzzy topological spaces and X is product related to Y, then their fuzzy topological product is almost compact.     

模糊系统及其通用性

本文应用Ｓｔｏｎｅ－Ｗｅｉｅｒｓｔｒａｓｓ定理证明了一类结构为普遍的模糊系统可以任意精度上逼近一实连函数。文章最后也证明了以此系统构成的模糊控制器是通用控制器。