Fell-拓扑的伪紧性（英文）

设X是拓扑空间，CL（X）表示X的所有非空闭子集的族，本文得到了下述结果：在CL（X）上的Fell-拓扑是伪肾的当且仅当X是feebly-紧或者非局部紧或者非σ－紧，由此得到了对于伪紧性不是闭遗传的两类新的拓扑空间。     

点是Gδ-集的∑*-空间的构成定理

在林寿与我最近合作的一篇文章中指出了∑*-空间的构成定理需重新考虑.本文就是要证明在空间X的每个点是Gδ-集的条件下该构成定理是成立的,所得的结论是:X是T1且每个点是Gδ-集的∑*-空间,如果f:X→Y是闭的满连续映射,则在Y中有一σ-闭离散子空间Z,使得对每个y∈Y\Z,f-1(y)是X的w1-紧子空间.为得到该主要结果,本文证明了若空间X是每个点是Gδ-集的次亚紧空间.则X中的每个闭离散子集是X中的Gδ-集.     

几类特殊的BCI代数

本文给出具有散子代数的ＢＣＩ代数的条件，讨论了Ｌ（Ｘ）为Ｘ的理想的ＢＣＩ代数，完全刻划了每个子代数都是理想的ＢＣＩ代数。     

6p阶可解对称图的分类

设ｘ是简单无向图，Ｇ是Ａｕｔ（Ｘ）的一个于群，Ｘ称为Ｇ－对称的，如果Ｇ在ｘ的１－孤（即两相邻顶点构成的有序偶）集合上的作用是传递的；ｘ称为对称图，如果Ｘ是Ａｕｔ（ｘ）－对称的；ｘ称为可解对称的，如果Ａｕｔ（Ｘ）包含可解子群Ｇ，使Ｘ是Ｇ－对称的．本文给出了具有６Ｐ个顶点的可解对称图的一个分类，这里ｐ≥５是素数．     

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.     

Topological continuous convergence

Let X be a limit space, Y a topological space. We show that c(X,Y), the limitierung of continuous convergence on LIM(X,Y), is topological whenever X is basic locally compact. For regular Y, local compactness of X is sufficient. In both cases, c(X,Y) coincides with the compact-open topology. If X satisfies a certain regularity condition, the fact that c(X,Y) is topological implies, conversely, that X is (basic) locally compact.The author would like to thank S. Weck for some inspiring discussions.     

一类广义变换半群的格林关系

设X是一个全序集,E是X上的一个凸等价关系．令 OE（X）={f∈TE（X）：Ax,y∈X,x≤y→f（x）≤f（y））, 其中TE（X）是E-保持变换半群．对于取定的θ∈OE（X）,在OE（X）上定义运算fog=fθg,使OE（X）成为广义半群OE（X;θ）．对于有限全序集X上的凸等价关系E,本文刻画了广义半群OE（X;θ）的正则元,描述了这个半群的格林关系．     

保持序和等价关系的自然偏序变换半群

设X为一个集合,■_X为X上的全变换半群.设E是X上的一个等价关系,定义T_E(X)={f∈■_X:■(x,y)∈E,(f(x),f(y))∈E},则T_E(X)是由等价关系E所确定的■_X的子半群.本文中,所考虑的集合X是一个有限全序集,同时E是非平凡的且所有的E-类都是凸集.显然■_E(X)={f∈T_E(X):■_x,y∈X,x≤y蕴涵f(x)≤f(y)}是T_E(X)的一个子半群.我们赋予■_E(X)自然偏序并讨论何时■_E(X)中的两个元素是关于这个偏序是相关的,然后确定■_E(X)中那些关于≤是相容的元素.此外,还描述了极大(极小)元和覆盖元.     

The hyperspace of the regions below of all lattice-value continuous maps and its Hilbert cube compactification

Let L be a continuous semilattice. We use USC(X, L) to denote the family of all lower closed sets including X × {0} in the product space X × AL and ↓1 C(X,L) the one of the regions below of all continuous maps from X to AL. USC(X, L) with the Vietoris topology is a topological space and ↓C(X, L) is its subspace. It will be proved that, if X is an infinite locally connected compactum and AL is an AR, then USC(X, L) is homeomorphic to [-1,1]ω. Furthermore, if L is the product of countably many intervals, then ↓ C(X, L) is homotopy dense in USC(X,L), that is, there exists a homotopy h : USC(X,L) × [0,1] →USC(X,L) such that h0 = idUSC(X,L) and ht(USC(X,L)) C↓C(X,L) for any t > 0. But ↓C(X, L) is not completely metrizable.     

关于周期吸附系统的分布混沌的注记

设X是一个紧致度量空间,f X→X是一个连续映射.若存在f的一个m-周期点p和另一个m'-周期点q(p≠q),使得对任意非空开集V(C)X,都有{p,q}(C)∞ Un=0fn(V),则称动力系统(X,f)是一个(m,m')型周期吸附系统.证明了:1)若(X,f)是一个(m,m')型周期吸附系统且X是自密的,则对任一给定的正整数k,存在一个fk的的分布混沌集S,使得S与X的任一非空开集之交均含有一个Cantor集;2)若(X,f)是一个(m,m')型周期吸附系统且拓扑共轭于(X ',f'),则(X ',f')也是一个(m,m')型周期吸附系统.改进和推广了已有结果.     

正规可数仿紧空间的逆极限

得到了如下结果:设X是逆系统{Xα,παβ,Λ}的逆极限,|Λ|=λ,假设每个映射πα∶X→Xα是开的且到上的,X是λ-仿紧,每个Xα是正规可数仿紧的,则X是正规可数仿紧的.进一步得到了关于遗传正规且遗传可数仿紧空间的类似结果.     

The Gerbe Of Higgs Bundles

The purpose of this work is to describe the (category of) Higgs bundles on a scheme X/C having a given cameral cover \bar{X}. We show that this category is a T \bar{X} gerbe, where T \bar{X} is a certain sheaf of abelian groups on X, and we describe the class of this gerbe precisely. In particular, it follows that the set of isomorphism classes of Higgs bundles with a fixed cameral cover \bar{X} is a torsor over the group H¹(X, T \bar{X}) which itself parametrizes T \bar{X} torsors on X. This underlying group H¹(X, T \bar{X}) can be described as a generalized Prym variety, whose connected component is either an abelian variety or a degenerate abelian variety. The main part of the work deals with abstract Higgs bundles; in the last two sections we derive the applications to Higgs bundles valued in a line bundle K and to bundles on elliptic fibrations.     

同伦群和上同调群的上乘积

<正> 在[1]中,作者研究了一个(N—1)维连通空间的同伦群和同调群的密切关系,那里所考虑的同伦群的维数是在(2N—2)以内,本文可以看成[1]的继续,我偿将考虑维数在(2N—1)以上而又在(3N—3)以下的同伦群,Betti 数;和上乘积的密切关系.我们     

Domain函数空间上Isbell拓扑与Scott拓扑何时相同

本文证明了,若L是一个双完备的连续DCPO,则对所有的RW-空间X,函数空间[X→L]上的Isbell拓扑和Scott拓扑相同当且仅当L是有最小元的L-Domain.而且还证明了,若X是核紧的局部连通空间,则对所有有最小元的连续L-DomainL,[X→L]上的Isbell拓扑和Scott拓扑相同当且仅当X是RW-空间.特别地,若X是连续DCPO,则对所有有最小元的连续L-DomainL,函数空间[X→L]上的Isbell拓扑和Scott拓扑相同当且仅当X是RW-空间.这也给出由Lawson和Mislove提出的一个公开问题的一个部分回答.     

Evaluation of the Assistant Function with Four Zeros and all Nonprincipal Characters but X1X2X3X4

To obtain a better Vinogradov's bound, assistant function with two or three zeros and all Dirichlet's characters has been evaluated. Assistant function g(X1,X2,X3,X4)with four zeros and all nonprincipal characters but X1X2X3X4 is constructed and evaluated in the paper. And the constant obtained is 8.395 511 841 994.     

关于凸子集和（绝对）收缩核

讨论了线性度量空间中凸子集在什么情况下为该空间的收缩核，以及在什么情况下为绝对收缩核。     

Agreeable domains

An integral domain D with quotient field K is defined to be agreeable if for each fractional ideal F of D[X] with F C K[X] there exists 0 = s ε D with sF C D[X]. D is agreeable ? D satisfies property (*) (for 0 ^ f(X) G K[X], there exists 0 = s ε D so that f(X)g(X) ε D[X] for g(X) ε K[X] implies that sg(X) ε D[X]) &; D[X] is an almost principal domain, i.e., for each nonzero ideal I of D[X] with IK[X] = K[X], there exists f(X) ε I and 0 = s ε D with sI C (f(X)). If D is Noetherian or integrally closed, then D is agreeable. A number of other characterizations of agreeable domains are given as are a number of stability properties. For example, if D is agreeable, so is ?^αD_{P α} and for a pair of domains D?D′ with a [DD:′]≠0, D is agreeable?D′ is agreeable. Results on agreeable domains are used to give an alternative treatment of Querre's characterization of divisorial ideals in integrally closed polynomial rings. Finally, the various characterizations of D being agreeable are considered for polynomial rings in several variables.     

论局部乘积与POINCARE-ALEXANDER-LEFSCHETZ型对偶定理

<正> 在§1我们界说了局部乘积,它关联 Hausdorff 紧致空间 X 中闭子集X_0的同调以及 X_0在 X 中邻域的同调.在流形与有边流形上的 Poincaré-Alexander-Lefschetz 型对偶定理可以用这种局部乘积表示(§2).在§3,我们研讨了一类所谓摹流形状空间.局部的下调群与上调群的概念在 [3,233—263页;8]中曾不明显地使     

Ritt’s theorem and the Heins map in hyperbolic complex manifolds

Let X be a Kobayashi hyperbolic complex manifold, and assume that X does not contain compact complex submanifolds of positive dimension (e.g., X Stein). We shall prove the following generalization of Ritt’s theorem: every holomorphic self-map f:X→X such that f(X) is relatively compact in X has a unique fixed point τ(f) ∈ X, which is attracting. Furthermore, we shall prove that τ(f) depends holomorphically on f in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author.     

Spaces with a Souslin and a shanin condition

If X is a regular hereditary Souslin space and x ∈X then either there exists a sequence {x_n: n=1, 2, ...} ? X{x} such that x ∈ [{x_n∶n=1, 2, ...}], or the pseudocharacter of x in X is no greater than countable. In other words, if X is a hereditary Souslin bicompactum which is a χ-space, then X is a Frechet-Urysohn space.