广义n-赋范空间中的Vogt定理

本文推广Vogt定理到广义n-赋范空间,即证明了两个广义n-赋范空间之间的保持ρ-诱导距离映射是仿射的.     

n-维赋范空间单位球极小球覆盖数2n-1与包含等距同构于(Rn,|| ||∞)的子空间

证明了对于-个n-维赋范空间X,如果b#=2n-1,则它一定包含一个与(Rn,|| ||∞)等距同构的子空间.     

n-维赋范空间单位球极小球覆盖数2n-1与包含等距同构于（R^n-1，‖‖∞）的子空间

证明了对于一个n-维赋范空间X，如果b#=2n-1，则它一定包含一个与（R^n-1，‖‖∞）等距同构的子空间．     

内积空间中的h-强凸集值映射

本文首先在赋范线性空间中引入一类广义强凸集值映射,称之为h-强凸集值映射.其次利用R?dstr?m消去律研究了h-强凸集值映射的一些基本性质.最后,给出h-强凸集值映射形式下赋范线性空间为内积空间的刻画条件.     

强E-凸性下赋范空间为内积空间的刻画

首先在赋范线性空间中引入了一类广义强凸集值映射,称之为强E-凸集值映射.其次利用Radstr?m消去律研究了强E-凸集值映射的一些基本性质.最后,给出了强E-凸集值映射形式下赋范线性空间为内积空间的刻画条件.     

赋范线性空间多目标规划的 广义KT-真有效解

对于赋范线性空间中的多目标规划问题,引进了广义KT-真有效解的概念.在一定条件下,得到了广义KT-真有效解和广义H-局部真有效解之间的关系.     

关于Fuzzy赋范空间的若干问题（Ⅱ）

在1984年,吴从炘、方锦暄和A.K.Katsaras分别提出了两种Fuzzy赋范空间的定义。这些概念既是赋范空间概念的自然推广,又是特殊的Fuzzy拓扑线性空间。在文[3～5]中,不仅考察了这两种定义之间的关系,还讨论了Fuzzy赋范空间的性质以及其上广义Fuzzy线性算子的连续性等。在本文中,我们将继文[4]给出Fuzzy赋范空间中子集有界性、稠密性的刻划条件并利用这些条件给出Fuzzy范数是诱出的充要条件。此外,作为诱出Fuzzy范数的推广,我们给出了两类Fuzzy范数的特征刻划。     

概率度量空间的等距度量化

本文给出了概率度量空间等距同构于度量空间及一类伪度量族生成空间的充要条件;给出了概率赋范空间等距同构于赋范空间、赋B₀型准范空间及可赋准范空间的充要条件。     

时滞矩阵微分方程的等度稳定性

在矩阵值范数定义的广义赋范空间上利用矩阵Liapunov泛函研究了时滞矩阵微分方程的等度稳定性,得出了若干新结果.     

L-模糊赋范空间的完备化

本文探讨L-模糊赋范空间的完备化问题.首先给出L-模糊赋范空间中L-模糊点列的柯西列和完备空间的概念,然后定义了两个L-模糊赋范空间之间的等距同构以及LX中层层一致稠密的集合,最后证明了每个L-模糊赋范空间在等距同构意义下有唯一的完备L-模糊赋范空间.     

Calderón-Zygmund-Type Operators on Weighted Weak Hardy Spaces over ℝn

We introduce certain Calderón-Zygmund-type operators and discuss their boundedness on spaces such as weighted Lebesgue spaces, weighted weak Lebesgue spaces, weighted Hardy spaces and weighted weak Hardy spaces. The sharpness of some results is also investigated. Received December 1, 1998, Revised May 2, 1999, Accepted May 19, 1999     

On Function Spaces with Mixed Norms — A Survey

The targets of this article are threefold. The first one is to give a survey on the recent developments of function spaces with mixed norms, including mixed Lebesgue spaces, iterated weak Lebesgue spaces, weak mixed-norm Lebesgue spaces and mixed Morrey spaces as well as anisotropic mixed-norm Hardy spaces. The second one is to provide a detailed proof for a useful inequality about mixed Lebesgue norms and the Hardy–Littlewood maximal operator and also to improve some known results on the maximal function characterizations of anisotropic mixed-norm Hardy spaces and the boundedness of Calderón–Zygmund operators from these anisotropic mixed-norm Hardy spaces to themselves or to mixed Lebesgue spaces. The last one is to correct some errors and seal some gaps existing in the known articles.     

Infinite distributive laws versus local connectedness and compactness properties

Various local connectedness and compactness properties of topological spaces are characterized by higher degrees of distributivity for their lattices of open (or closed) sets, and conversely. For example, those topological spaces for which not only the lattice of open sets but also that of closed sets is a frame, are described by the existence of web neighborhood bases, where webs are certain specific path-connected sets. Such spaces are called web spaces. The even better linked wide web spaces are characterized by F-distributivity of their topologies, and the worldwide web spaces (or C-spaces) by complete distributivity of their topologies. Similarly, strongly locally connected spaces and locally hypercompact spaces are characterized by suitable infinite distributive laws. The web space concepts are also viewed as natural extensions of spaces that are semilattices with respect to the specialization order and have continuous (unary, binary or infinitary) semilattice operations.     

Transitivities of maps of general topological spaces

In this paper we investigate orbit-transitivity, strong orbit-transitivity, ω-transitivity and open-set-transitivity of maps of general topological spaces. The relation between these transitivities is studied. We discuss various topological spaces, containing pseudo-regular spaces, partially completable spaces, and topological spaces without quasi-isolated points. Several conditions on spaces and on continuity for one transitivity to imply another transitivity are given.     

A Mazur–Ulam theorem in non-Archimedean normed spaces

The classical Mazur–Ulam theorem which states that every surjective isometry between real normed spaces is affine is not valid for non-Archimedean normed spaces. In this paper, we establish a Mazur–Ulam theorem in the non-Archimedean strictly convex normed spaces.     

Compact and precompact sets in asymmetric locally convex spaces

The aim of the present paper is to study precompactness and compactness within the framework of asymmetric locally convex spaces, defined and studied by the author in [S. Cobza?, Asymmetric locally convex spaces, Int. J. Math. Math. Sci. 2005 (16) (2005) 2585-2608]. The obtained results extend some results on compactness in asymmetric normed spaces proved by [L.M. García-Raffi, Compactness and finite dimension in asymmetric normed linear spaces, Topology Appl. 153 (2005) 844-853], and [C. Alegre, I. Ferrando, L.M. García-Raffi, E.A. Sánchez-Pérez, Compactness in asymmetric normed spaces, Topology Appl. 155 (6) (2008) 527-539].     

On convergence determining and separating classes of functions

Herein, we generalize and extend some standard results on the separation and convergence of probability measures. We use homeomorphism-based methods and work on incomplete metric spaces, Skorokhod spaces, Lusin spaces or general topological spaces. Our contributions are twofold: we dramatically simplify the proofs of several basic results in weak convergence theory and, concurrently, extend these results to apply more immediately in a number of settings, including on Lusin spaces.     

Statistical convergence in topology

We introduce and investigate statistical convergence in topological and uniform spaces and show how this convergence can be applied to selection principles theory, function spaces and hyperspaces.     

Dimension zero at all scales

We consider the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the category of (unbounded) separable metric spaces and (metrically proper) uniform maps. A unified treatment is given to the large scale dimension and the small scale dimension. We show that in all categories a space has dimension zero if and only if it is equivalent to an ultrametric space. Also, 0-dimensional spaces are characterized by means of retractions to subspaces. There is a universal zero-dimensional space in all categories. In the Lipschitz Category spaces of dimension zero are characterized by means of extensions of maps to the unit 0-sphere. Any countable group of asymptotic dimension zero is coarsely equivalent to a direct sum of cyclic groups. We construct uncountably many examples of coarsely inequivalent ultrametric spaces.