共查询到10条相似文献,搜索用时 31 毫秒
1.
For a topological space X we denote by CL(X) the collection of all nonempty closed subsets of X. Suppose we have a map T which assigns in some coherent way to every topological space X some topology T(X) on CL(X). In this paper we study continuity and inverse continuity of the map iA,X :(CL(A),T{A)) → (CL(X),T(X)) defined by iA,x(F) = F whenever F ∈CL(A), for various assignment T; in particular, for locally finite topology, upper Kuratowski topology, and Attouch-Wets topology, etc. 相似文献
2.
Chen ShuTao Hudzik Henryk Kowalewski Wojciech Wang YuWen Wisła Marek 《中国科学A辑(英文版)》2008,51(2):293-303
First we prove that the approximative compactness of a nonempty set C in a normed linear space can be reformulated equivalently in another way.It is known that if C is a semi-Chebyshev closed and approximately compact set in a Banach space X,then the metric projectorπC from X onto C is continuous.Under the assumption that X is midpoint locally uniformly rotund,we prove that the approximative compactness of C is also necessary for the continuity of the projectorπC by the method of geometry of Banach spaces.Using this general result we find some necessary and sufficient conditions for T to have a continuous Moore-Penrose metric generalized inverse T~ ,where T is a bounded linear operator from an approximative compact and a rotund Banach space X into a midpoint locally uniformly rotund Banach space Y. 相似文献
3.
Certain topological relationships between the topological spaces and the spaces of their subsets have heen studied in[1],[4]and[5].In this paper we Will discuss other topological relationships between the topological spaces and their hyperspaces with the Vietoris topology. Let (X,T) be a topological space, 相似文献
4.
The Factor Decomposition Theorem of Bounded Generalized Inverse Modules and Their Topological Continuity 总被引:1,自引:0,他引:1
Lun Chuan ZHANG 《数学学报(英文版)》2007,23(8):1413-1418
In this paper we obtain a Douglas type factor decomposition theorem about certain important bounded module maps. Thus, we come to the discussion of the topological continuity of bounded generalized inverse module maps. Let X be a topological space, x →Tx : X→L(E) be a continuous map, and each R(Tx) be a closed submodule in E, for every fixed x C X. Then the map x→ Tx^+: X→L(E) is continuous if and only if ||Tx^+|| is locally bounded, where Tx^+ is the bounded generalized inverse module map of Tx. Furthermore, this is equivalent to the following statement: For each x0 in X, there exists a neighborhood ∪0 at x0 and a positive number λ such that (0, λ^2)lohtatn in ∩x∈∪0C/σ(Tx^+Tx), where a(T) denotes the spectrum of operator T. 相似文献
5.
Fibrewise topological spaces theory,presented in the recent 20 years,is a new branch of mathematics developed on the basis of General Topology,Algebra topology and Fibrewise spaces theory.It is associated with differential geometry,Lie groups and dynamical systems theory.From the perspective of Category theory,it is in the higher category of general topological space,so the discussion of new properties and characteristics of the variety of fibre topological space has more important significance.This paper introduces the process of the origin and development of Fibrewise topological spaces theory.Then,we study the main contents and important results in this branch.Finally,we review the research status of Fibrewise topological spaces theory and some important topics. 相似文献
6.
7.
Topological Anosov Maps of Non-compact Metric Spaces 总被引:2,自引:0,他引:2
Let X be a metric space. We say that a continuous surjection f: X→X is a topological Anosov map (abbrev. TA-map) if f is expansive and has pseudo-orbit tracing property with respect to some compatible metric for X. This paper studies the properties of TA-maps of non-compact metric spaces and gives some conditions for the map to be topologically mixing. 相似文献
8.
In this paper, we introduce the concept of statistically sequentially quotient map:A mapping f : X → Y is statistically sequentially quotient map if whenever a convergent sequence S in Y, there is a convergent sequence L in X such that f(L) is statistically dense in S. Also, we discuss the relation between statistically sequentially quotient map and covering maps by characterizing statistically sequentially quotient map and we prove that every closed and statistically sequentially quotient image of a g-metrizable space is g-metrizable. Moreover,we discuss about the preservation of generalization of metric space in terms of weakbases and sn-networks by closed and statistically sequentially quotient map. 相似文献
9.
Let S={1,1/2,1/2 2,…,1/∞=0} and I = [0,1] be the unit interval. We use ↓USC(S) and ↓C(5) to denote the families of the regions below of all upper semi-continuous maps and of the regions below of all continuous maps from S to I and ↓C0(S) ={↓f∈↓C(S):f(0)=0}.↓USC(S) endowed with the Vietoris topology is a topological space. A pair of topological spaces (X, Y) means that X is a topological space and Y is its subspace. Two pairs of topological spaces (X, Y) and (A, B) are called pair-homeomorphic (≈) if there exists a homeomorphism h:X→A from X onto A such that h{Y) = B. It is proved that, (↓USC(S), ↓C0(S))≈(Q,s) and (↓USC(5), ↓C(5)\↓C0(S))≈(Q,c0), where Q =[-1, l]ω is the Hilbert cube and s=(-1,1)ω, c0 = {(xn)∈Q:lim n→∞ xn=0}. But we do not know what (↓USC(S),↓C(5)) is. 相似文献
10.
An equilibrium version of set-valued Ekeland variational principle and its applications to set-valued vector equilibrium problems
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Jing Hui Qiu 《数学学报(英文版)》2017,33(2):210-234
By using Gerstewitz functions, we establish a new equilibrium version of Ekeland variational principle, which improves the related results by weakening both the lower boundedness and the lower semi-continuity of the ob jective bimaps. Applying the new version of Ekeland principle, we obtain some existence theorems on solutions for set-valued vector equilibrium problems, where the most used assumption on compactness of domains is weakened. In the setting of complete metric spaces(Z,d), we present an existence result of solutions for set-valued vector equilibrium problems, which only requires that the domain XZ is countably compact in any Hausdorff topology weaker than that induced by d. When(Z, d) is a Féchet space(i.e., a complete metrizable locally convex space), our existence result only requires that the domain XZ is weakly compact. Furthermore, in the setting of non-compact domains, we deduce several existence theorems on solutions for set-valued vector equilibrium problems,which extend and improve the related known results. 相似文献