相对Meso紧空间及相对Meso-Lindeloff空间

定义了相对meso紧空间、相对meso-Lindeloff空间的概念,研究了相对meso紧、相对meso-Lindeloff空间在闭Lindeloff映射、完备映射下的性质.     

一种新的可数紧性

在L-fuzzy拓扑空间上，研究了可数S^＊-紧和可数S-紧的相关性质和特征。并就可数S^＊-紧、可数S-紧以及S-Lindeloef性质三者之间的关系进行了研究，得到了满足S-Lindeloef性质的可数S^＊-紧空间为S^＊-紧空间等结论。     

Helton类算子及单值扩张性质（英文）

本文研究了Helton类算子在紧摄动下单值扩张性质的稳定性,同时研究了2×2上三角算子矩阵在紧摄动下单值扩张性质的稳定性.利用半Fredholm域的特点,获得了2×2上三角算子矩阵具有单值扩张性质的稳定性的充分必要条件.     

Helton类算子及单值扩张性质

本文研究了Helton类算子在紧摄动下单值扩张性质的稳定性, 同时研究了2×2上三角算子矩阵在紧摄动下单值扩张性质的稳定性. 利用半Fredholm域的特点, 获得了2×2上三角算子矩阵具有单值扩张性质的稳定性的充分必要条件.     

L-拓扑空间的相对S~*-紧性

在L-拓扑空间中引入了相对S*-紧性的概念,证明了相对S*-紧性是相对闭遗传的、弱同胚不变的和L-好的推广等性质,并证明了相对S*-紧性的T ychonoff定理是成立的。     

几类非紧性测度之间的比较性质

首先列举了几类不同意义下的非紧性测度,并对这几种非紧性测度作了比较,得到了两个重要的比较性质.     

性质M_F与拟连续Domain中的Scott上紧集

对拟连续domain引入了关于基的性质MF,证明了对拟连续domain P,任两个Scott紧上集的交是Scott紧当且仅当P关于某一(任一)基具有性质MF.     

只有一个B—函数的完备黎曼流形

讨论了只有一个Ｂｕｓｅｍａｎｎ函数的完备非紧黎曼流形的几何拓扑性质。     

关于具有紧邻域扩充性质的拓扑空间

在此文中我们得到如下结论：１）每个具有紧邻域扩充性质的可逼近紧空间是绝对邻域收缩核；２）每个具有紧邻域扩充性质的局部紧空间是绝对邻域收缩核。     

拓扑线性空间中的Drop定理与Drop性质

给出了拓扑线性空间中的一个Drop定理.利用此Drop定理,证明了拓扑线性空间中的每个序列紧凸集具有Drop性质;每个可数紧闭凸集具有拟Drop性质.而且结出了拓扑线性空间中Drop性质和拟Drop性质的序列流特征.也讨论了Drop性质和拟Drop性质与泛函取极值之间的联系.     

On the difference property of the family of functions with the Baire property

We show that it is consistent with ZFC that the family of functions with the Baire property has the difference property. That is, every function for which f(x + h)-f(x) has the Baire property for every h∈R is of the form f=g + Awhere g has the Baire property and A is additive. This revised version was published online in June 2006 with corrections to the Cover Date.     

Weak and quasi approximation properties in Banach spaces

In this paper, we introduce weak versions (the weak approximation property, the bounded weak approximation property, and the quasi approximation property) of the approximation property and derive various characterizations of these properties. And we show that if the dual of a Banach space X has the weak approximation property (respectively the bounded weak approximation property), then X itself has the weak approximation property (respectively the bounded weak approximation property). Also we observe that the bounded weak approximation property is closely related to the quasi approximation property.     

The strong approximation property and the weak bounded approximation property

We show that the strong approximation property (strong AP) (respectively, strong CAP) and the weak bounded approximation property (respectively, weak BCAP) are equivalent for every Banach space. This gives a negative answer to Oja's conjecture. As a consequence, we show that each of the spaces _c0$c_0$ and _?1${?}_1$ has a subspace which has the AP but fails to have the strong AP.     

On relations between weak approximation properties and their inheritances to subspaces

It is shown that for the separable dual X^∗ of a Banach space X, if X^∗ has the weak approximation property, then X^∗ has the metric weak approximation property. We introduce the properties W^∗D and MW^∗D for Banach spaces. Suppose that M is a closed subspace of a Banach space X such that M^⊥ is complemented in the dual space X^∗, where for all m∈M}. Then it is shown that if a Banach space X has the weak approximation property and W^∗D (respectively, metric weak approximation property and MW^∗D), then M has the weak approximation property (respectively, bounded weak approximation property).     

Boundary Properties of Factorial Classes of Graphs

For a class of graphs X, let be the number of graphs with vertex set in the class X, also known as the speed of X. It is known that in the family of hereditary classes (i.e. those that are closed under taking induced subgraphs) the speeds constitute discrete layers and the first four lower layers are constant, polynomial, exponential, and factorial. For each of these four layers a complete list of minimal classes is available, and this information allows to provide a global structural characterization for the first three of them. The minimal layer for which no such characterization is known is the factorial one. A possible approach to obtaining such a characterization could be through identifying all minimal superfactorial classes. However, no such class is known and possibly no such class exists. To overcome this difficulty, we employ the notion of boundary classes that has been recently introduced to study algorithmic graph problems and reveal the first few boundary classes for the factorial layer.     

A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement

We get the following result. A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement. We positively answer a question of the strongly paracompact property.     

Compact adjoint operators and approximation properties

This paper is concerned with the space of all compact adjoint operators from dual spaces of Banach spaces into dual spaces of Banach spaces and approximation properties. For some topology on the space of all bounded linear operators from separable dual spaces of Banach spaces into dual spaces of Banach spaces, it is shown that if a bounded linear operator is approximated by a net of compact adjoint operators, then the operator can be approximated by a sequence of compact adjoint operators whose operator norms are less than or equal to the operator norm of the operator. Also we obtain applications of the theory and, in particular, apply the theory to approximation properties.     

Making doughnuts of Cohen reals

For a ? b ? ω with b\ a infinite, the set D = {x ∈ [ω]^ω : a ? x ? b} is called a doughnut. A set S ? [ω]^ω has the doughnut property ?? if it contains or is disjoint from a doughnut. It is known that not every set S ? [ω]^ω has the doughnut property, but S has the doughnut property if it has the Baire property ?? or the Ramsey property ?. In this paper it is shown that a finite support iteration of length ω₁ of Cohen forcing, starting from L , yields a model for CH + (??) + (??) + (?).     

THE ANALYTIC KREIN-MILMAN PROPERTY IN BANACH SPACES

In[1],A.V.BuknvalovandA.A.Danilevichhaveintroducedtheanalyticcordon--NikodylllpropertyincompleXBanacllspacesastheanalyticallalogueoftilewellknowllRadoll-NikodylllpropertyconcerningtherealgeometricalstrllcturesofBanachspaces.LetXbeacomplexBanachspace,XissaidtohavetheanalyticRadon--Nikodymproperty(analyticRNP,illshort)ifforeveryuniformlyboundedanalyticfunctiollffromtheopenunitdiscDofCwitllvaluesinX,f:D~X,fhasradiallimitsa.e.onthetornsT=={e*':0E[0,Zx]}illX,tllisllleallsthatfora.e.e6[0,…     

Dual problems for weak and quasi approximation properties

It is shown that for the separable dual X^∗ of a Banach space X if X^∗ has the weak approximation property, then X has the metric quasi approximation property. Using this it is shown that for the separable dual X^∗ of a Banach space X the quasi approximation property and metric quasi approximation property are inherited from X^∗ to X and for a separable and reflexive Banach space X, X having the weak approximation property, bounded weak approximation property, quasi approximation property, metric weak approximation property, and metric quasi approximation property are equivalent. Also it is shown that the weak approximation property, bounded weak approximation property, and quasi approximation property are not inherited from a Banach space X to X^∗.