局部凸分离空间上的Caratheodory-Hahn-Kluvanek延拓定理

运用测度理论的方法将Banach空间上的Caratheodory-Hahn-Kluvanek延拓定理作进一步研究.首先在局部凸空间中引入P完备、分离等概念,并讨论P完备的局部凸分离空间上的Caratheodory-Hahn-Kluvanek延拓定理,进而给出Banach空间族的乘积空间上的Caratheodory-Hahn-Kluvanek延拓定理.     

度量凸函数的延拓

每个度量空间都能等距嵌入到实Banach空间,所以度量凸函数可视为Banach空间子集上的函数．本文举出反例说明不是所有度量凸函数都能延拓为凸函数,并给出度量凸函数能延拓为凸函数的充分条件．     

复域双周期Riccati方程解空间极限集的复杂性

研究了一个复域上双周期系数的Riccati方程,证明了其解空间可分成三个不相交的子空间,其中一个子空间为闭集,所有周期解的全解析延拓的闭包包含在这个子空间内并形成一个完备子集。该子集在解的延拓变换群下是最小不变闭集,可能具有分形结构,而任一周期解的全解析延拓均在此子集内稠密。     

AL~p-空间(1＜p＜∞)的单位球面间的非满等距映射的延拓

在本文中,我们证明AL~p_-空间(1相似文献   

基于模糊伪度量的Riesz空间值模糊测度空间的完备化

本文研究了模糊测度在模糊集上的延拓问题,得出了在广义正则条件下取值于Riesz空间子集的每一个模糊测度都可以唯一地从广义模糊σ-环延拓到由其生成的模糊σ-域的结论。利用我们所提出的模糊伪度量,得到了实现Riesz空间值对称模糊测度空间完备化的拓扑方法。     

等距线性延拓问题

本文引入了两个赋范空间的单位球面间等距映射的延拓问题,并且列出了相关问题的一些重要结果和近期的进展.     

广义延拓矩阵在乘法扰动下特征空间的相对扰动界

在矩阵A与其扰动矩阵A有相同分块的谱分解下,对于以A为母矩阵的广义延拓矩阵凡（A）及以A为母矩阵的广义延拓矩阵凡（A）,使用特征值双分离度方法,给出了广义延拓矩阵n（A）与其扰动矩阵n（A）的特征空间在乘法扰动下的相对扰动界．     

二维严格凸赋范空间单位球面间等距映射的线性延拓

主要研究二维严格凸实赋范空间E和F的单位球面S_1(E)和S_1(F)之间的等距映射的线性延拓问题.利用二维严格凸赋范空间单位球面的性质得到:若等距映射V_0:S_1(E)→S_1(F)满足一定条件,则V_0可延拓为全空间E上的线性等距映射V:E→F.     

AL-空间单位球面上的等距算子的延拓

证明了AL-空间和Banach空间单位球面之间的满等距算子均可以延拓为全空间上的线性等距算子.     

锥b-度量空间中关于扩张映射的一些不动点定理（英文）

本文证明锥b-度量空间中关于扩张映射的一些不动点定理,没有考虑映射的连续性和锥的正规性.其结果不仅推广了锥度量空间,度量空间和b-度量空间中的相关结果,而且也延拓和补充了先前的一些结果.此外,我们给出几个例子验证了其结论.     

Extension conditions for bounded linear and sublinear operators with values in lindenstrauss spaces

We find extension conditions for linear and sublinear operators with values in four classes of spaces: the spaces of continuous functions on a compact set, Lindenstrauss spaces, and their separable parts. We prove that in all these cases the extension property for linear operators implies the extension property for sublinear operators, while in separable spaces the two properties are equivalent.     

Approximate extension property of mappings

The extension problem is to determine the extendability of a mapping defined on a closed subset of a space into a nice space such as a CW complex over the whole space. In this paper, we consider the extension problem when the codomains are general spaces. We take a shape theoretic approach to generalize the extension theory so that the codomains are allowed to be general spaces. We extend the notion of extension type which has been defined for the class of CW complexes and introduce the notion of approximate extension type which is defined for general spaces. We define approximate extension dimension analogously to extension dimension, replacing the class of CW complexes by the class of finitistic separable metrizable spaces. For every metrizable space X, we show the existence of approximate extension dimension of X.     

Essential extensions of Hausdorff spaces

In the category Haus of Hausdorff spaces the only injectives are the one-point spaces. Even though every Hausdorff spaceX has a maximal essential extension,X fails to have an injective hull, providedX has more than one point. A non-empty Hausdorff space has a proper essential extension if and only ifX is locally H-closed but not H-closed. In this case,X has (up to isomorphism) precisely one proper essential extension: the Obreanu-Porter extension (being simultaneously its maximal essential extension and its minimal H-closed extension). Completely parallel results hold for the categories SReg, Reg, and Tych of semi-regular, regular, and completely regular spaces respectively. In particular, the Alexandroff compactifications of locally compact, non-compact Hausdorff spaces are characterized categorically as the proper essential extensions of non-empty spaces in Tych (resp. Reg).Dedicated to my friend Nico Pumplün on his sixtieth birthday     

On Strict Extensions of Nearness Spaces

Strict extensions of nearness spaces are constructed as spaces of round Cauchy filters. Morita's simple extension is identified as the strict extension generated by Morita-generated filters. Carlson's B-completeness is compared with Herrlich completeness and completeness of Morita T-uniformities. The three completeness concepts are shown to be equivalent in regular nearness spaces.     

On adjunctions between Lim, SL-Top, and SL-Lim

Consider (L,*,1) be a commutative, strictly two-sided quantale with the underlying lattice L being meet-continuous. Two adjunctions, one is between limit spaces and stratified L-limit spaces and the other is between stratified L-limit spaces and stratified L-topological spaces, are established. The first adjunction can be viewed as an extension of Lowen's adjunction between the category of topological spaces and stratified [0,1]-topological spaces. The second is an extension of an adjunction between limit spaces and (stratified) L-topological spaces established in U. Höhle and T. Kubiak (Höhle-Kubiak, Semigroup Forum (2007)).     

Infinite-Dimensional Calculus Under Weak Spatial Regularity of the Processes

Two generalizations of Itô formula to infinite-dimensional spaces are given. The first one, in Hilbert spaces, extends the classical one by taking advantage of cancellations when they occur in examples and it is applied to the case of a group generator. The second one, based on the previous one and a limit procedure, is an Itô formula in a special class of Banach spaces having a product structure with the noise in a Hilbert component; again the key point is the extension due to a cancellation. This extension to Banach spaces and in particular the specific cancellation are motivated by path-dependent Itô calculus.     

Uniformity Structures on L-Fuzzy Spaces

We extend the notion of a uniform space in a natural way by defining a uniform spaces in L-fuzzy spaces.Although these spaces seem quite similar to ordinary case,we show that the category of this uniform spaces is a good extension of the category of ordinary uniform spaces and the category of L-uniform spaces.Moreover,we introduce the concept of uniform topological spaces in the framework of uniform spaces in L-fuzzy spaces.Furthermore,the relation between proximity and uniform spaces in L-fuzzy spaces will...     

Banach空间上集值测度与模糊数测度的扩张

在Banach空间上,给出集值测度的扩张定理并借助集测度的扩张给出了模糊数测度的扩张定理。     

FUZZY PRETOPOLOGICAL SPACES, AN EXTENSIONAL TOPOLOGICAL EXTENSION OF FTS

O.Introduction'ByacrazytopologyonasetXwemeanasubsetofixwhichisclosedunderfiniteintersections,arbitraryulilonsandcolltainsalltheconstantfuZzysets.ItiswellknownthatthecategoryFTSoffuzzytopologicalspacesisawell--fibredtopologicalconstruct,andsinceitcoDtainsthecategoryTopasabothreflectiveandcoreflectivesubcategory)likeTOP,thiscategorylacksmanyconvenientpropertiessuchasextensionality(fordefinitionsee[6]or4.1inthispaper),cartesianclosednessandbeingatopologicaluniverse(see[1,6]fordefinitons).SoH…     

On Stein's extension operator preserving Sobolev–Morrey spaces

We prove that Stein's extension operator preserves Sobolev–Morrey spaces, that is spaces of functions with weak derivatives in Morrey spaces. The analysis concerns classical and generalized Morrey spaces on bounded and unbounded domains with Lipschitz boundaries in the n‐dimensional Euclidean space.