关于H?lder正则性的一个注记

Holder正则性在图像消噪、信号重构等方面都具有重要意义．本文对Holder空间的两种定义进行研究分析,利用归纳法和Littlewood—Paley分解方法证明了两种Ho1der定义在一定条件下还是等价的,为Holder正则性的应用提供了理论依据．     

关于S-Lindelof 空间及其子空间

本文是在半开集理论中提出了S-Lindelf空间的概念.指出S-Lindelf空间是S-紧空间的一种推广,并对该空间及其子空间所具有的性质进行了一些有益的讨论.     

关于Nordgren的一个问题

本文证明了存在有界线性算子T使得T的弱预解集(WR(T)不是线性的,这回答了[1]中Nordgren等提出的一个未解决的问题。同时我们还讨论了有关WR(T)的若干基本性质。     

关于Ginsburg & Woods的一个问题

构造了一个反例回答了基数不等式|X|<2^c(X)Δ(X)不仅对于正则空间类不成立,甚至对Tychonoff空间类亦不成立。     

关于一个奇异Dirichlet问题的注记

The Dirichlet problem to a second order differential equation with some singularities is studied. Some existence results are established to the problem which generalize some results recently obtained by D. O‘Regan by eliminating some superfluous constrains to the problem. Also, some new results have been proven which may provide more useful information for the study of the problem.     

关于分层空间度量化的一个问题

利用g-函数研究广义度量空间和度量化,统一了近年来许多有趣的工作.本文回答了[2]中提出的一个问题.所讨论的拓扑空间是正则的.     

具有非平凡Fourier型Banach空间的一个特征

设X为复Banach空间,则X具有非平凡Fourier型当且仅当存在(等价地,对所有)0 <α <1,任取f∈C^α([0,2π];X)满足f(0)=f(2π),都有■成立.     

I(L)型诱导空间的可数性

本文证明了(L^X,δ)与其I(L)型诱导空间(I(L)^X,ω(δ))的权,特征,浓度.Lindel?f度相等,(L^X,δ)为Lindel?f空间当且仅当(I(L)^X,σ(δ))为Lindel?f空间,且给出了(L^X,δ)与(I(L^X)ω(δ))的稠密集,稀疏集,第一纲集,第二纲集,Baire性质之间的关系.     

Remarks on discretely absolutely star-Lindelöf spaces

In this paper, we prove the following statements(1) There exists a Hausdorff Lindelöf space X such that the Alexandroff duplicate A(X) of X is not discretely absolutely star-Lindelöf.(2) If X is a regular Lindelöf space, then A(X) is discretely absolutely star-Lindelöf.(3) If X is a normal discretely star-Lindelöf space with e(X) < ω ₁, then A(X) is discretely absolutely star-Lindelöf.     

对GOOD关于Hausdorff维数的一个问题的推广

我们证明了有无穷多个     

On relatively weakly almost Lindelöf subsets

Summary A subset Y of a space X is weakly almost Lindel?f in X if for every open cover U of X, there exists a countable subfamily V of U such that Y ⊆ comp (∩V ). We investigate the relationship between relatively weakly almost Lindel?f subsets and relatively almost Lindel?f subsets, and also study various properties of relatively weakly almost Lindel?f subsets.     

On relatively almost Lindelöf subsets

We introduce the concept of relatively almost Lindelöf subsets as a generalization of almost Lindelöf subspaces. We study various properties of relatively almost Lindelöf subsets and investigate the relationship between relatively almost Lindelöf subsets and almost Lindelöf subspaces. A special interest is given to spaces X in which almost Lindelöf subsets relative to X are closed.     

On I-Lindelöf sets

A space (X, T) is called I-Lindelöf [1] if every cover A of X by regular closed subsets of the space (X, T) contains a countable subfamily A′ such that X = ∪{int (A): A ∈ A′}. In this work we introduce the class of I-Lindelöf sets as a proper subclass of rc-Lindelöf sets [3]. We study various properties of I-Lindelöf sets and investigate the relationship between I-Lindelöf sets and I-Lindelöf subspaces. We give a new characterization of I-Lindelöf spaces in terms of this type of sets. Also, we study spaces (X, T) in which every I-Lindelöf set in (X, T) is closed.     

On Dense Subspaces Satisfying Stronger Separation Axioms

We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of -weight less than has a dense completely Hausdorff (and hence Urysohn) subspace. We show that there exists a Tychonoff space without dense normal subspaces and give other examples of spaces without "good" dense subsets.     

Properties of prealmost α-continuous and presemi-weakly continuous functions

Some properties of two classes of functions (p.a.α.c. and p.s.w.c) are studied. This revised version was published online in June 2006 with corrections to the Cover Date.     

Spaces with large relative extent

In this paper, we prove the following statements: (1) For every regular uncountable cardinal κ, there exist a Tychonoff space X and Y a subspace of X such that Y is both relatively absolute star-Lindelöf and relative property (a) in X and e(Y, X) ? κ, but Y is not strongly relative star-Lindelöf in X and X is not star-Lindelöf. (2) There exist a Tychonoff space X and a subspace Y of X such that Y is strongly relative star-Lindelöf in X (hence, relative star-Lindelöf), but Y is not absolutely relative star-Lindelöf in X.     

拟相似集的Hausdorff测度的特征

Siegfried GRAF在文献［1］中给出了自相似集上的Hausdorff测度(简称H-测度)的特征.John McLaughlin在文献［2］中引入了拟相似集的概念,K.J.Falconer又在文献［3］中讨论了拟相似集上H-测度和维数的性质.本文研究拟相似集上的H-测度的特征,并得出在一定条件下支撑于其上满足一定条件的测度与H-测度的等价性条件.