广义近似空间的粗糙同胚与拓扑同胚

对广义近似空间之间的映射引入并刻画了粗糙连续性和拓扑连续性,探讨了他们的性质及相互关系.证明了两个粗糙连续映射的复合还是粗糙连续的,每个粗糙连续的映射都是拓扑连续的.在此基础上引入了粗糙同胚性质和拓扑同胚性质的概念,证明了拓扑同胚性质均为粗糙同胚性质并考察了广义近似空间的诸如分离性、连通性、紧性等的粗糙同胚不变性和拓扑同胚不变性.     

Connectedness of Cone-Efficient Solution Set for Cone-Quasiconvex Multiobjective Programming in Locally Convex Spaces

This paper deals with the connectedness of the cone-efficient solution set for vector optimization inlocally convex Hausdorff topological vector spaces.The connectedness of the cone-efficient solution set is provedfor multiobjective programming defined by a continuous cone-quasiconvex mapping on a compact convex set ofalternatives.The generalized saddle theorem plays a key role in the proof.     

L─Fuzzy拓扑空间的局部连通性

文［１］曾在广义拓扑分子格中提出了一种连通性。本文在Ｌ—ｆｕｚｚｙ拓扑空间中给出了这种连通性的几种刻划，并引入了Ｌ—ｆｙｚｚｙ拓扑空间的局部连通性。这种局部连通性是有限可乘的，商序同态保持的且是好的推广。另外，ｆｕｚｚｙ实直线是局部连通的。     

拓扑向量空间中锥拟凸多目标规划锥有效解集的连通性(英文)

本文研究局部凸的拓扑向量空间中锥拟凸多目标规划锥有效解集的连通性问题.证明了定义在紧凸集上目标映射为一对一的锥拟凸多目标规划的锥有效解集是连通的.在证明中,广义鞍点定理起着关键的作用.     

关于子基的强连通性

在LF拓扑空间中借助于相对闭包引入了关于子基的强连通性的概念,研究了它的一些基本性质和等价刻画.结果表明,这种强连通性保持了LF拓扑空间中已有连通性的许多类似性质     

New Generalized R-KKM Type Theorems in General Topological Spaces and Applications

In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature.     

拓扑序空间中的广义向量值均衡问题

利用一个KKM型定理,在拓扑序空间中,建立了关于广义向量值均衡问题解的某些新的存在性定理.     

拓扑向量空间中锥拟凸多目标规划锥有效解集的连通性

本文研究局部凸的Hausdorff拓扑向量空间中锥拟凸多目标规划锥有效解集的连通性问题。利用广义鞍点定理,证明了目标映射为一对一的锥拟凸多目标规划的锥有效解集是连通的。     

Generalized KKM-type theorems for weakly generalized KKM mapping with some applications

In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.     

A Generalization of Herrlich's Question on Almost Reflective and Coreflective Subclasses of Top and Unif

H. Herrlich asked in Topology Appl. 49 (1993), 251–264, whether there are nontrivial classes of topological spaces that are almost reflective and almost coreflective at the same time. This question was dealt with (in Huek and Tozzi, Appl. Categ. Structures 4 (1996), 57–68) in a more general setting than almost reflective and almost coreflective classes. The present paper investigates a modified question: when a nontrivial generalized reflective class of topological or uniform spaces is equivalent to a generalized coreflective class of spaces.     

On Convex Generalized Systems

In this paper, the set-convexity and mapping-convexity properties of the extended images of generalized systems are considered. By using these image properties and tools of topological linear spaces, separation schemes ensuring the impossibility of generalized systems are developed. Then, special problem classes are investigated.     

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.     

拓扑空间上的KKM定理,不动点定理,广义变分不等式

引进没有任何凸结构的拓扑空间上的广义R-KKM映射的定义并利用古典的KKM原理得到一般拓扑空间上的KKM型定理以及若干个变形结果,然后作为应用给出了非紧的拓扑空间上不动点定理和广义变分不等式解的存在性定理.     

Collective fixed points, generalized games and systems of generalized quasi-variational inclusion problems in topological spaces

In this paper, by using a fixed point theorem for expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces due to the author, we first prove a collective fixed point theorem and an existence theorem of equilibrium points for a generalized game. As applications, some new existence theorems of solutions for systems of generalized quasi-variational inclusion problems are established in noncompact topological spaces. Our results are different from known results in the literature.     

开广义序同态的刻划及拓扑分子格的特征与权

王国俊先生于〔１〕中借助闭元成功地引入了开广义序同态的概念。本文给出了开广义序同态的一个刻划并对其是否增加拓扑分子格的权与特征等问题进行了研究，得到了积拓扑分子格的特征与权与因子拓扑分子格的特征与权间的关系，从而部分回答了ＬＦ拓扑中关于特征的两个公开问题。     

Connectedness of the Set of Efficient Solutions for Generalized Systems

We introduce the concept of positive proper efficient solutions to the generalized system in this paper. We show that, under some suitable conditions, the set of positive proper efficient solutions is dense in the set of efficient solutions to the generalized system. We discuss also the connectedness of the set of efficient solutions for the generalized system with monotone bifunctions in real locally convex Hausdorff topological vector spaces. This research was partially supported by the National Natural Science Foundation of China (10561007), the Natural Science Foundation of Jiangxi Province, China, and a grant from the National Science Council of ROC.     

新型拓扑KKM定理与等价形式及其应用

在不具线性结构拓扑空间—广义区间空间—中得到了新型拓扑KKM定理及其几个等价形式.作为应用,本文研究了广义区间空间中一类抽象形式变分不等式解的存在性问题.     

Essential Components of the Set of Weakly Pareto-Nash Equilibrium Points for Multiobjective Generalized Games in Two Different Topological Spaces

In this paper, we study the existence and essential components of the set of weakly Pareto-Nash equilibrium points for multiobjective generalized games in two different uniform topological spaces. We obtain some new existence theorems. Examples show that the results are not identical in two different topological spaces.The author thanks two referees for careful reading of the paper and helpful comments.     

乘积拓扑矢量空间中的不动点定理和广义矢量平衡问题组

利用零调映象的一个不动点定理,在乘积拓扑矢量空间内得到了某些新的不动点定理,作为应用,在乘积拓扑矢量空间内,对一类广义矢量平衡问题组证明了一些平衡存在性定理,这些定理推广了近期文献中的一些重要的已知结果.     

The Set-Valued Dynamic System and Its Applications to Pareto Optima

In this paper, we first study the existence of endpoints for set-valued dynamic systems which are either upper or lower semicontinuous in metric spaces. Then the existence, uniqueness and algorithms of endpoints for set-valued dynamic systems which are either generalized contractions (defined in metric spaces) or topological contractions (defined in topological spaces which do not necessarily have any metric). These results are then applied to derive the existence of Pareto optima for mappings which take values in ordered Banach spaces. Finally, the stability of (generalized) nucleolus sets is also established.