共查询到17条相似文献,搜索用时 99 毫秒
1.
In this paper, for 1 < p < ∞, the authors show that the coarse ?
p
-Novikov
conjecture holds for metric spaces with bounded geometry which are coarsely embeddable
into a Banach space with Kasparov-Yu’s Property (H). 相似文献
2.
Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the persistence approximation property for maximal Roe algebras. They show that persistence approximation property of maximal Roe algebras follows from maximal coarse Baum-Connes conjecture. In particular, let X be a discrete metric space with bounded geometry, assume that X admits a fibred coar... 相似文献
3.
The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu's property A, the ideal structure of the Roe algebra of X with coefficients in B(H) is completely characterized by the ideal families of weighted subspaces of X, where B(H) denotes the C*-algebra of bounded linear operators on a separable Hilbert space H. 相似文献
4.
A metric space(X, d) is called bi-Lipschitz homogeneous if for any points x, y ∈ X,there exists a self-homeomorphism h of X such that both h and h-1are Lipschitz and h(x) = y.Let 2(X,d)denote the family of all non-empty compact subsets of metric space(X, d) with the Hausdorff metric. In 1985, Hohti proved that 2([0,1],d)is not bi-Lipschitz homogeneous, where d is the standard metric on [0, 1]. We extend this result in two aspects. One is that 2([0,1],e)is not bi-Lipschitz homogeneous for an admissible metric e satisfying some conditions. Another is that 2(X,d)is not bi-Lipschitz homogeneous if(X, d) has a nonempty open subspace which is isometric to an open subspace of m-dimensional Euclidean space Rm. 相似文献
5.
In this note,we present that:(1)Let X=σ{Xα:α∈A} be|A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1. 相似文献
6.
In this paper, we take the case of soft points into consideration and propose a new metric structure called soft Da-metric space for a specific orbit defined with soft points. In order to establish fixed point results in the modified metric space, we modify a few existing definitions in the sense of soft points. 相似文献
7.
In this note,we present that:(1)Let X=σ{Xα:α∈A} be|A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1. 相似文献
8.
The authors introduce a kind of slowly increasing cohomology HS*(X) for a discrete metric space X with polynomial growth,and construct a character map from the slowly increasing cohomology HS*(X) into HC*cont(S(X)),the continuous cyclic cohomology of the smooth subalgebra S(X) of the uniform Roe algebra B*(X).As an application,it is shown that the fundamental cocycle,associated with a uniformly contractible complete Riemannian manifold M with polynomial volume growth and polynomial contractibility radius growth,is slowly increasing. 相似文献
9.
10.
A discrete dynamical system can be expressed as xn 1 =f(xn), n=0,1, 2,... where X isa metric space and f : X→X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). 相似文献
11.
Piotr W. Nowak 《Journal of Functional Analysis》2007,252(1):126-136
We study Guoliang Yu's Property A and construct metric spaces which do not satisfy Property A but embed coarsely into the Hilbert space. 相似文献
12.
In this work, the authors introduce the concept of
$(p,q)$-quasi-contraction mapping in a cone metric space. We prove
the existence and uniqueness of a fixed point for a
$(p,q)$-quasi-contraction mapping in a complete cone metric space.
The results of this paper generalize and unify further fixed point
theorems for quasi-contraction, convex contraction mappings and
two-sided convex contraction of order $2$. 相似文献
13.
函数空间SUF的RNP与模糊上鞅 总被引:1,自引:0,他引:1
本文证明取值于度量空间的函数的Bochner积分与Aumann积分是等价的,且积分值相等。空间的Radon-Nikodym性质(简称RNP)在正线性等距映射下保持不变。在此基础上得到空间SUF具有RNP,且把诸结果应用于模糊上秧的研究,得到了模糊上鞅的几个收敛定理。 相似文献
14.
In this paper, we study a class of vector minimization problems on a complete metric space X which is identified with the corresponding complete metric space of objective functions
. We do not impose any compactness assumption on X. We show that, for most (in the sense of Baire category) functions
, the corresponding vector optimization problem has a solution. 相似文献
15.
Vladimir Anashin 《Mathematics in Computer Science》2012,6(4):375-393
In the paper, we study behaviour of discrete dynamical systems (automata) w.r.t. transitivity; that is, speaking loosely, we consider how diverse may be behaviour of the system w.r.t. variety of word transformations performed by the system: we call a system completely transitive if, given arbitrary pair a, b of finite words that have equal lengths, the system ${\mathfrak{A}}$ , while evolution during (discrete) time, at a certain moment transforms a into b. To every system ${\mathfrak{A}}$ , we put into a correspondence a family ${\mathcal{F}_{\mathfrak{A}}}$ of continuous mappings of a suitable non-Archimedean metric space and show that the system is completely transitive if and only if the family ${\mathcal{F}_{\mathfrak{A}}}$ is ergodic w.r.t. the Haar measure; then we find easy-to-verify conditions the system must satisfy to be completely transitive. The theory can be applied to analyse behaviour of straight-line computer programs (in particular, pseudo-random number generators that are used in cryptography and simulations) since basic CPU instructions (both numerical and logical) can be considered as continuous mappings of a (non-Archimedean) metric space ${\mathbb{Z}_{2}}$ of 2-adic integers. 相似文献
16.
Yair Bartal Nathan Linial Manor Mendel Assaf Naor 《Discrete and Computational Geometry》2005,33(1):27-41
In this note we consider the metric Ramsey problem for the normed
spaces $\ell_p$. Namely, given some $1\le p \le \infty$ and
$\alpha \ge 1$, and an integer $n$, we ask for the largest $m$
such that every $n$-point metric space contains an $m$-point
subspace which embeds into $\ell_p$ with distortion at most $
\alpha$. In [1] it is shown that in the case of $\ell_2$,
the dependence of $m$ on $\alpha$ undergoes a phase transition at
$\alpha =2$. Here we consider this problem for other $\ell_p$, and
specifically the occurrence of a phase transition for $p\neq 2$.
It is shown that a phase transition does occur at $\alpha=2$ for every $p\in
[1,2]$. For $p > 2$ we are unable to determine the answer, but
estimates are provided for the possible location of such a phase
transition. We also study the analogous problem for isometric
embedding and show that for every $1 < p < \infty$ there are
arbitrarily large metric spaces, no four points of which embed
isometrically in $\ell_p$. 相似文献
17.
本文研究了强零维度量空间,借助点星弱邻域网刻画了强零维度量空间,获得了强零维度量空间等价于具有离散覆盖列的点星弱邻域网的非空正则空间,回答了葛英提出的一个问题. 相似文献