集值映射空间上的■0特征1

应用k-网的概念证明了:若X,Y为■0空间且Y为局部紧的,则X到Y上满足条件(G)的点紧致的族连续集值映射族依紧开拓扑是■0空间.     

集值映射空间在紧开拓扑下的NO性质

本文讨论了点紧致的连续集值映射空间在赋予紧开拓扑下的某些拓扑性质,证明了:若X,Y为NO空间,则X到Y上的点紧致的连续集值映射族依紧开拓扑是NO空间,从而将Michael[1]的结论推广到更大的映射空间类上.     

集值映射空间在紧开拓扑下的N_0性质

本文讨论了点紧致的连续集值映射空间在赋予紧开拓扑下的某些拓扑性质,证明了:若X,Y为N_0空间,则X到Y上的点紧致的连续集值映射族依紧开拓扑是N_0空间,从而将Michael的结论推广到更大的映射空间类上.     

集值映射空间上的(ξ)0特征

应用k-网的概念证明了:若X,Y为(ξ)0空间且Y为局部紧的,则X到Y上满足条件(G)的点紧致的族连续集值映射族依紧开拓扑是(ξ)0空间.     

序列覆盖的闭映射保持可度量性

设f:X→Y是连续的满映射. f称为序列覆盖映射,若{y})是Y中的收敛序列,则存在X中的收敛序列{xn},使得每一xn∈f-1(yn);f称为1序列覆盖映射,若对于每-y∈Y,存在x∈f-1(y),使得如果{yn}是Y中收敛于点y的序列,则有X中收敛于点x的序列{xn},使得每一xn∈f-1(yn).本文研究度量空间序列覆盖的闭映射之构造,否定地回答了Topology and its Applications上提出的一个问题.     

Lipschitz映射的下方图形

令(X,d)是紧的度量空间,用↓USC(X)和↓LIP(X)分别表示从X到I所有的上半连续映射和所有Lipschitz映射的下方图形的全体．本文证明如果X是一个无限的紧的度量空间,则(↓USC(X),↓LIP(X))≈(Q,B(Q)),其中B(Q)=Q\(-1,1)~ω是Hilbert立方体Q=[-1,1]~ω的伪边界．     

局部同胚成为有限覆盖映射的充要条件

本文考察了局部同胚成为有限覆盖映射的充要条件。特别,作为本文结果的一个推论。 设X与Y是两个Hausdorff空间,f是X到Y的一个局部同胚。如果Y道路连通且包含至少两个点,则以下条件是彼此等价的: (1)f是有限覆盖映射, (2)f是正常映射, (3)f是闭映射。 它推广和改进了F. E. Browder, R. S. Palais及陈文(山原)等人的相应结果。     

两个映射定理

本文证明了:(1)设f是正规,等紧(isocompact)空间X到空间Y上的闭映射,则f是紧覆盖映射;(2)设f是正规,等紧空间X到Fréchet空间Y上的闭映射,则存在闭子集X′(?)X使f|x′是X′到Y上的既约映射;分别改进了Michael、Lanev映射定理,并利用(1)得到“闭映射保持正规、k-半分层性”以改进Lutzer关于k-半分层空间的映射定理。     

可数对一映射及相关问题

本文研究了■0-sn-度量空间与度量空间之间的关系.利用特殊映射,获得了在序列空间中下述命题等价:(1)空间X是■0-sn-度量空间;(2)存在从度量空间M到X可数对一、序列商、σ映射f;(3)存在从度量空间M到X可数对一、序列商、σ映射f使得对每一个x∈X,■f-1(x)是σ-紧.推广了参考文献[3,4]中的一些结果.     

关于度量空间的开几乎s映像（英文）

Arhangel'skiǐ引入几乎s映射的概念:从拓扑空间X到拓扑空间Y上的映射f称为几乎s映射,若y是Y的非孤立点,则f~(-1)(y)是X的可分集.本文研究几乎s映射、近似s映射与边缘s映射之间的基本关系,得到了度量空间的开几乎s映像的内在刻画,并且讨论了度量空间上可数双商边缘s映射的性质.     

度量空间的序列覆盖边界紧映象(英文)

本文主要讨论了度量空间的序列覆盖边界紧映象.用序列商、序列覆盖或1-序列覆盖的纤维边界紧或有限来刻画具有sn网或弱基的空间.主要结果如下:(1)度量空间上的序列覆盖边界紧映射是1-序列覆盖映射;(2)空间X是度量空间的序列商边界紧映象当且仅当X是snf-第一可数空间;(3)空间X是度量空间的序列覆盖边界紧S映象当且仅当X有点可数sn-网.     

一致覆盖和度量空间的紧映象

本文利用一致覆盖的概念,讨论了度量空间的序列覆盖紧映象的结构.主要结果有: (1)空间X是局部可分度量空间的序列覆盖紧映象当且仅当X具有由cosmic子空间构成的一致sn网; (2)空间X是局部可分度量空间的序列覆盖,商紧映象当且仅当X是度量空间的序列覆盖,商紧映象且是局部cosmic空间.     

Metric complements of overt closed sets

We show that the set of points of an overt closed subspace of a metric completion of a Bishop‐locally compact metric space is located. Consequently, if the subspace is, moreover, compact, then its collection of points is Bishop‐compact. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Local Currents in Metric Spaces

Ambrosio and Kirchheim presented a theory of currents with finite mass in complete metric spaces. We develop a variant of the theory that does not rely on a finite mass condition, closely paralleling the classical Federer–Fleming theory. If the underlying metric space is an open subset of a Euclidean space, we obtain a natural chain monomorphism from general metric currents to general classical currents whose image contains the locally flat chains and which restricts to an isomorphism for locally normal currents. We give a detailed exposition of the slicing theory for locally normal currents with respect to locally Lipschitz maps, including the rectifiable slices theorem, and of the compactness theorem for locally integral currents in locally compact metric spaces, assuming only standard results from analysis and measure theory.     

度量空间的弱开cs-映象的注记

In this paper, we prove that a space with a compact countable weak base if and only if it is a weak open cs-image of a metric space.     

Distributional chaos in a sequence

In this paper we prove a sufficient condition for the continuous map of a compact metric space for being distributively chaotic in a sequence. As an application, it is proved that a continuous map of an interval is chaotic in the Li–Yorke sense if and only if it is distributively chaotic in a sequence.     

Metric spaces in synthetic topology

We investigate the relationship between the synthetic approach to topology, in which every set is equipped with an intrinsic topology, and constructive theory of metric spaces. We relate the synthetic notion of compactness of Cantor space to Brouwer’s Fan Principle. We show that the intrinsic and metric topologies of complete separable metric spaces coincide if they do so for Baire space. In Russian Constructivism the match between synthetic and metric topology breaks down, as even a very simple complete totally bounded space fails to be compact, and its topology is strictly finer than the metric topology. In contrast, in Brouwer’s intuitionism synthetic and metric notions of topology and compactness agree.     

度量投影的收敛性（英文）

讨论了赋范空间中度量投影的收敛性．得到了在局部紧集控制下，Chebyshev凸集序列的度量投影的收敛性与K－M收敛，Wijsman收敛和Kuratowski收敛都等价．本文的结论完善了M．Tsukada在[1]和[2]结果．     

Optimal Mutual Location of Compact Sets in Spaces Endowed with Euclidean Invariant Gromov–Hausdorif Metric

Non–empty compact subsets of the Euclidean space located optimally (i.e., the Hausdorff distance between them cannot be decreased) are studied. It is shown that if one of them is a single point, then it is located at the Chebyshev center of the other one. Many other particular cases are considered too. As an application, it is proved that each three–point metric space cari be isometrically embedded into the orbit space of the group of proper motions acting on the compact subsets of the Euclidean space. In addition, it is proved that for each pair of optimally located compact subsets all intermediate compact sets in the sense of Hausdorff metric are also intermediate in the sense of Euclidean Gromov–Hausdorff metric.     

Symmetries of Contact Metric Manifolds

We study the Lie algebra of infinitesimal isometries on compact Sasakian and K-contact manifolds. On a Sasakian manifold which is not a space form or 3-Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian structure. For a manifold with K-contact structure, we prove that there exists a Killing vector field of constant length which is not an infinitesimal automorphism of the structure if and only if the manifold is obtained from the Konishi bundle of a compact pseudo-Riemannian quaternion-Kähler manifold after changing the sign of the metric on a maximal negative distribution. We also prove that nonregular Sasakian manifolds are not homogeneous and construct examples with cohomogeneity one. Using these results we obtain in the last section the classification of all homogeneous Sasakian manifolds.