The connectedness of the solutions set for generalized vector equilibrium problems

In this paper, we establish the connectedness of the sets of Henig efficient solutions, globally efficient solutions, weak efficient solutions, superefficient solutions and efficient solutions for a class of generalized vector equilibrium problems without the assumptions of monotonicity and compactness.     

无限维空间拟凸映射多目标最优化问题解集的连通性

本文在一个无限格中引入了拟凸、强拟凸和严格拟凸映射。并在约束集为紧凸条件下，证明了相应的多目标规划问题之有效解集和弱有效解集连通性结果。     

An example of a nonarcwise connected rim-countable locally connected continuum

An example of a rim-countable, locally connected, but nonarcwise connected continuum is constructed, which is important for the classification of locally connected continua. The point of interest in this result is that there are no metrizable locally connected continua with the above properties. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 659–666, May, 1999.     

Linear and Nonlinear Effects in Connectedness Structure: Comparison between European Stock Markets

The purpose of this research is to compare the risk transfer structure in Central and Eastern European and Western European stock markets during the 2007–2009 financial crisis and the COVID-19 pandemic. Similar to the global financial crisis (GFC), the spread of coronavirus (COVID-19) created a significant level of risk, causing investors to suffer losses in a very short period of time. We use a variety of methods, including nonstandard like mutual information and transfer entropy. The results that we obtained indicate that there are significant nonlinear correlations in the capital markets that can be practically applied for investment portfolio optimization. From an investor perspective, our findings suggest that in the wake of global crisis and pandemic outbreak, the benefits of diversification will be limited by the transfer of funds between developed and developing country markets. Our study provides an insight into the risk transfer theory in developed and emerging markets as well as a cutting-edge methodology designed for analyzing the connectedness of markets. We contribute to the studies which have examined the different stock markets’ response to different turbulences. The study confirms that specific market effects can still play a significant role because of the interconnection of different sectors of the global economy.     

路拟凸多目标最优化问题解集的连通性

在多目标最优化理论中,研究解集的拓扑结构是一个有意义的重要课题,而解集的连通性问题又是结构理论中一个重要分支。本文提出一类路拟凸多目标最优化问题,就此讨论了有效解集和弱有效解集或者是连通的,或者是路连通的。这对拟凸最优化问题关于解集的连通性,已经刻划得比较深刻     

连通度量空间的映象

拓扑空间X称为s连通,若X不能表示为两个非空的不相交的序列开集之并.本文纠正了A.Fedeli 和A.Le Donne关于连通度量空间映象的错误论证,证明了s连通性可刻画为连通度量空间的连续的序列覆盖映象,从而导出连通的序列空间(或FrEchet空间)可刻画为连通度量空间的商映象(或伪开映象),回答了V.V.Tkachuk在Proc.Amer.Math Soc.上提出的问题.     

Topological ordered C- (resp. I-)spaces and generalized metric spaces

The following result due to Hanai, Morita, and Stone is well known: Let f be a closed continuous map of a metric space X onto a topological space Y. Then the following statements are equivalent: (i) Y satisfies the first countability axiom; (ii) for each y∈Y, f−1{y} has a compact boundary in X; (iii) Y is metrizable.In this article we obtain several related results in the setting of topological ordered spaces. In particular we investigate the upper and lower topologies of metrizable topological ordered spaces which are both C- and I-spaces in the sense of Priestley.     

Intersection Theorems with a Continuum of Intersection Points

In all existing intersection theorems, conditions are given under which a certain subset of a collection of sets has a nonempty intersection. In this paper, conditions are formulated under which the intersection is a continuum of points satisfying some interesting topological properties. In this sense, the intersection theorems considered in this paper belong to a new class. The intersection theorems are formulated on the unit cube and it is shown that both the vector of zeroes and the vector of ones lie in the same component of the intersection. An interesting application concerns the model of an economy with price rigidities. Using the intersection theorems of this paper, it is easily shown that there exists a continuum of zero points in such a model. The intersection theorems treated give a generalization of the well-known lemmas of Knaster, Kuratowski, and Mazurkiewicz (Ref. 1), Scarf (Ref. 2), Shapley (Ref. 3), and Ichiishi (Ref. 4). Moreover, the results can be used to sharpen the usual formulation of the Scarf lemma on the cube.     

A Link Between Two Connectedness Notions

The composition of two previously introduced Galois connections is used to provide a wider perspective on the Clementino–Tholen connectedness versus separation Galois connection. Moreover, a link between this and Castellini's connectedness–disconnectednes Galois connection is also presented.     

锥连续锥拟凹多目标规划问题弱有效解集的连通性

本文讨论了锥连续锥拟凹向量函数的弱有效解集的连通性问题；证明了当可行集X为紧凸集，目标函数f在X上锥连续锥拟凹时，其弱有效解集是连通的，在一定的意义下，改进了文献[1] 中的结果。