拓扑和的自同伦等价群

如果拓扑空间X,Y的拓扑和X∨Y的自同伦等价可以对角化,则X∨Y的自同伦等价群Aut(X∨Y)可表示为它的两个子群Autx(X∨Y)与AutY(X∨y)的乘积.     

Some Properties of Two Kinds of Multifunctions

Let X and Y be metrizable topological linear spaces.In this paper,the following results are proved:(1)If X and Y are complete,F;X→Y is a point closed u.s.c.,and symmetric process with ——↑F(X)=Y,then either F(X) is meager in Y,or else F is an open multifunction with F(X)=Y.(2)If X is complete,and F:X→Y is a process with a subclosed graph,then F is l.s.c..We also discuss topological multi-homomorphisms between topological linear spaces.     

关于有界线性算子的非紧测度的若干性质

利用非紧测度在商空间B(X,Y)/K(X,Y)上构造了一个范数,指出这一范数可由B(X,Y)上的某一范数生成.并且X或Y是Hilbert空间时,B(X,Y)/K(X,Y)上赋于这种范数时是完备的.另外,还建立了非紧测度与熵数,近似数之间的一些联系.     

关于CO-H-空间上的映射(Ⅰ)

对CO-H-空间X和Y,本文得到[X,Y]上的元素为有限阶元素的一个充分条件,并讨论了全体从X到Y的CO-H-映射的同伦等价类所组成的集合[X,Y]_(co-H)对[X,Y]上的加法运算封闭的条件.     

关于广义导算子的左右本性逆

在本文中,X、Y等表示Banach空间,H、K等表示Hilbert空间,如无特别注明均为无限维的。[X,Y]表示由X到Y的有界线性算子空间,当Y=X时记作B(X)。K(X)表示X上的紧算子全体所成之集。 设A_i∈B(X)、B_i∈B(Y)(i=1,2,…,n),由     

二维连续型随机变量函数的独立性探讨

给出了一种根据二维随机变量(X,Y)的密度函数f(x,y),构造相互独立的随机变量函数U=u(X,Y)和V=v(X,Y)的方法,丰富随机变量独立性的理论,探索X和Y的内在联系.     

夹心半群T(X,Y,θ)上的一个同余链

设T(X, Y,θ)是两个非空集合X, Y上的夹心半群,其中θ是从Y到X的一个映射.本文刻画了这个半群T(X, Y,θ)上的一些同余,得到了半群上的同余链.     

Moore-Penrose逆和Drazin逆的正则分解表示及其扰动

1引言及预备知识 设X,Y为Banach空间,B(X,Y)表示从X到Y中的有界线性算子组成的Banach空间.简记B(X,X)为B(X).对算子T∈B(X,Y),R(T)与N(T)分别表示T的值域和核空间.IP表示空间P上的恒等算子 定义1.1设T∈B(X,Y).若存在S∈B(Y,X),满足(1) TST=T;(2) ...     

关于co-H-空间上的映射(Ⅱ)

对于 co-H-空间 X 和 Y,本文对所有 X 到 Y 的 co-H-映射的同伦等价类所成的群[X,Y]~H([X,Y]的子群)的秧进行估值,得到如下结论:当 X 满足一定条件时ρ[X,Y]~H≤(?)β_K(X)β_k(Y)以及当取同纬映象结构时ρ[SX,SY]~H=(?)β_K(X)β_k(Y).另外本文还讨论了 co-H-空间和回路空间上的 F-等价问题,并获得一些结果.     

二元Block-Basu型指数分布的独立性与不相关性

若（X,Y）服从二元Block-Basu型指数分布,则X,Y相互独立与不相关是等价的．还给出了X,Y的相关系数和尾部相关系数．     

论附属于某种连续映像的不等式及其在纤维空间中的应用

<正> §1. 设 X,Y 为拓扑空间,又设 f:X→Y 为连续映像.J.H.C.Whitehead 证明 X,Y 为 CW 丛而 f 能导出基本群及上同调群间的同模对应时,f 为同伦对等映像.映像 f 是否存在,不仅与 X,Y 的基本群及上同调群的构造有关,而与 X,Y 内在的几何结构有密切的关系.连续照像 f 导出 X,Y 之间上同调群的准同模对应 f,那末 f 能与某些准同模对应相交换,由此 J.H.C.Whitehead 指出正则准同模的观念.由[4]可知正则同模论供应我们许多同伦不变量,它们是直接可以计算的东西,并且对于 X,Y 间连续映像的分类问题,应该有密切的关系.     

Regular-Norm Balls can be Closed in the Strong Operator Topology

The main results obtained are:– A Dedekind complete Banach lattice Y has a Fatou norm if and only if, for any Banach lattice X, the regular-norm unit ball Ur = {T Lr(X,Y): ||T||r 1} is closed in the strong operator topology on the space of all regular operators, Lr(X,Y).– A Dedekind complete Banach lattice Y has a norm which is both Fatou and Levi if and only if, for any Banach lattice X, the regular-norm unit ball Ur is closed in the strong operator topology on the space of all bounded operators, L(X,Y).– A Banach lattice Y has a Fatou–Levi norm if and only if for every L-space X the space L(X,Y) is a Banach lattice under the operator norm.– A Banach lattice Y is isometrically order isomorphic to C(S) with the supremum norm, for some Stonean space S, if and only if, for every Banach lattice X, L(X,Y) is a Banach lattice under the operator norm.Several examples demonstrating that the hypotheses may not be removed, as well as some applications of the results obtained to the spaces of operators are also given. For instance:– If X = Lp() and Y = Lq(), where 1 < p,q < , then Lr(X,Y) is a first category subset of L(X,Y).     

Stability Characterizations of ε-isometries on Certain Banach Spaces

Suppose that X, Y are two real Banach Spaces. We know that for a standard ε-isometry f : X → Y, the weak stability formula holds and by applying the formula we can induce a closed subspace N of *. In this paper, by using again the weak stability formula, we further show a sufficient and necessary condition for a standard ε-isometry to be stable in assuming that N is w*-closed in Y*.Making use of this result, we improve several known results including Figiel's theorem in reflexive spaces.We also prove that if, in addition, the space Y is quasi-reflexive and hereditarily indecomposable, then L(f)≡span[f(X)] contains a complemented linear isometric copy of X; Moreover, if X =Y, then for every e-isometry f: X → X, there exists a surjective linear isometry S:X → X such that f-S is uniformly bounded by 2ε on X.     

Models of Curves and Finite Covers

Let K be a discrete valuation field with ring of integers O _K .Letf : X ! Y be a finite morphism of curves over K. In this article, we study some possible relationships between the models over O K of X and of Y. Three such relationships are listed below. Consider a Galois cover f : X ! Y of degree prime to the characteristic of the residue field, with branch locus B. We show that if Y has semi-stable reduction over K,thenX achieves semi-stable reduction over some explicit tame extension of K.B/.WhenK is strictly henselian, we determine the minimal extension L=K with the property that X L has semi-stable reduction. Let f : X ! Y be a finite morphism, with g.Y/ > 2. We show that if X has a stable model X over O _K ,thenY has a stable model Y over O _K , and the morphism f extends to a morphism X ! Y. ! Y. Finally, given any finite morphism f : X ! Y, is it possible to choose suitable regular models X and Y of X and Y over O _K such that f extends to a finite morphism X ! Y ?As wasshown by Abhyankar, the answer is negative in general. We present counterexamples in rather general situ-ations, with f a cyclic cover of any order > 4. On the other hand, we prove, without any hypotheses on the residual characteristic, that this extension problem has a positive solution when f is cyclic of order 2 or 3.     

Banach空间中不适定线性算子方程的最佳逼近解

设X,Y为Banach空间,T为从X到Y的线性算子.T的值域R(T)≠Y且为逼近紧子空间,T的零空间N(T)≠{θ}.证得不适定算子方程Tx=y的最佳逼近解对任意y∈Y均存在的充分必要条件是N(T)为X的迫近子空间.     

Spaces of Densely Continuous Forms

The set C(X,Y) of continuous functions from a topological space X into a topological space Y is extended to the set D(X,Y) of densely continuous forms from X to Y, such form being a kind of multifunction from X to Y. The topologies of pointwise convergence, uniform convergence, and uniform convergence on compact sets are defined for D(X,Y), for locally compact spaces X and metric spaces Y having a metric satisfying the Heine–Borel property. Under these assumptions, D(X,Y) with the uniform topology is shown to be completely metrizable. In addition, if X is compact, D(X,Y) is completely metrizable under the topology of uniform convergence on compact sets. For this latter topology, an Ascoli theorem is established giving necessary and sufficient conditions for a subset of D(X,Y) to be compact.     

Division and k-th root theorems for Q-manifolds

We prove that a locally compact ANR-space X is a Q-manifold if and only if it has the Disjoint Disk Property (DDP), all points of X are homological Z∞-points and X has the countable-dimensional approximation property (cd-AP), which means that each map f:K→X of a compact polyhedron can be approximated by a map with the countable-dimensional image. As an application we prove that a space X with DDP and cd-AP is a Q-manifold if some finite power of X is a Q-manifold. If some finite power of a space X with cd-AP is a Q-manifold, then X2 and X×[0,1] are Q-manifolds as well. We construct a countable familyχof spaces with DDP and cd-AP such that no space X∈χis homeomorphic to the Hilbert cube Q whereas the product X×Y of any different spaces X, Y∈χis homeomorphic to Q. We also show that no uncountable familyχwith such properties exists.     

On Quantitative Sphere Equivalence and Extrapolation Phenomenon

Let X,Y be Banach spaces.We prove that if their unit spheres S(X)and S(Y)are(α,β)-H?lder homeomorphic for some α,β ∈(0,1].Then the unit spheres of Lp(Ω,μ,X)and ...