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111.
We prove that there exists a cohomology locally connected compact metrizable space which is not homology locally connected. In the category of compact Hausdorff spaces a similar result was proved earlier by G.E. Bredon. 相似文献
112.
A topological minimax theorem involving two functions is derived. It generalizes Greco and Horvath'minimax theorem given by them in 2002. 相似文献
113.
本文研究赋范线性空间中集值映射向量优化问题超有效解集的连通性问题.证明了目标映射为锥拟凸的向量优化问题的超有效解集是连通的. 相似文献
114.
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 相似文献
115.
116.
Summary We discuss the relationship between two different sequential connectedness, and prove that sequential connectedness is countably
multiplicative. 相似文献
117.
On the connectedness of the set of weakly efficient points of a vector optimization problem in locally convex spaces 总被引:7,自引:0,他引:7
S. Helbig 《Journal of Optimization Theory and Applications》1990,65(2):257-270
In vector optimization, topological properties of the set of efficient and weakly efficient points are of interest. In this paper, we study the connectedness of the setE
w
of all weakly efficient points of a subsetZ of a locally convex spaceX with respect to a continuous mappingp:X Y,Y locally convex and partially ordered by a closed, convex cone with nonempty interior. Under the general assumptions thatZ is convex and closed and thatp is a pointwise quasiconvex mapping (i.e., a generalized quasiconvex concept), the setE
w
is connected, if the lower level sets ofp are compact. Furthermore, we show some connectedness results on the efficient points and the efficient and weakly efficient outcomes. The considerations of this paper extend the previous results of Refs. 1–3. Moreover, some examples in vector approximation are given.The author is grateful to Dr. D. T. Luc and to a referee for pointing out an error in an earlier version of this paper. 相似文献
118.
We develop two different hierarchies of Kirkwood-Salsburg equations for the connectedness functions of random continuum percolation. These equations are derived by writing the Kirkwood-Salsburg equations for the distribution functions of thes-state continuum Potts model (CPM), taking thes1 limit, and forming appropriate linear combinations. The first hierarchy is satisfied by a subset of the connectedness functions used in previous studies. It gives rigorous, low-order bounds for the mean number of clusters n
c
and the two-point connectedness function. The second hierarchy is a closed set of equations satisfied by the generalized blocking functions, each of which is defined by the probability that a given set of connections between particles is absent. These auxiliary functions are shown to be a natural basis for calculating the properties of continuum percolation models. They are the objects naturally occurring in integral equations for percolation theory. Also, the standard connectedness functions can be written as linear combinations of them. Using our second Kirkwood-Salsburg hierarchy, we show the existence of an infinite sequence of rigorous, upper and lower bounds for all the quantities describing random percolation, including the mean cluster size and mean number of clusters. These equations also provide a rigorous lower bound for the radius of convergence of the virial series for the mean number of clusters. Most of the results obtained here can be readily extended to percolation models on lattices, and to models with positive (repulsive) pair potentials. 相似文献
119.
J. W. Nieuwenhuis 《Journal of Optimization Theory and Applications》1982,36(2):289-301
We will prove that, in the case where all the domination cones are closed and convex, have a nonempty interior, and are totally ordered with respect to inclusion, the set of weakly nondominated outcomes of a nonempty convex compact setY
R
n
is connected. Further, we give a relationship between weakly nondominated and nondominated solutions.The author would like to thank the referees for their valuable comments. 相似文献
120.
In general normed spaces,we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior.We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function.Moreover,we provide necessary and suffcient conditions about the existence of weak(sharp) Pareto solutions. 相似文献