关于不分明对称广义邻近空间的性质(英文)

关于不分明邻近空间的概念是由A .K .Katsaras给出的 ,本文在此基础上 ,首先引入了不分明对称广义邻近空间的概念 .然后研究了不分明对称广义邻近空间的性质 .最后给出了不分明对称广义邻近空间的乘积性和邻近连续性 .     

Positive one-parameter semigroups on ordered banach spaces

In this review we describe the basic structure of positive continuous one-parameter semigroups acting on ordered Banach spaces. The review is in two parts.First we discuss the general structure of ordered Banach spaces and their ordered duals. We examine normality and generation properties of the cones of positive elements with particular emphasis on monotone properties of the norm. The special cases of Banach lattices, order-unit spaces, and base-norm spaces, are also examined.Second we develop the theory of positive strongly continuous semigroups on ordered Banach spaces, and positive weak^*-continuous semigroups on the dual spaces. Initially we derive analogues of the Feller-Miyadera-Phillips and Hille-Yosida theorems on generation of positive semigroups. Subsequently we analyse strict positivity, irreducibility, and spectral properties, in parallel with the Perron-Frobenius theory of positive matrices.     

Selection properties of uniform and related structures

In this paper we present some results on selection properties in asymmetric generalized metric and uniform spaces. We demonstrate differences between selection properties of these spaces and selection properties of metric and uniform spaces.     

概率准度量族空间（英文）

引入了概率准度量族空间、概率准范数族空间、随机准度量族空间和随机准范数族空间的概念，包括了现有的各种相关空间类[1～11]（特别是[8，9]）作为特殊情况，建立了统一的空间体系．同时，我们研究了所引入的一般空间类的一些性质和拓扑结构．     

BMOA(R,m) and capacity density Bloch spaces on hyperbolic Riemann surfaces

We investigate a number of spaces of functions on Riemann surfaces which are related to Bloch spaces and functions of bounded mean oscillation (BMO). These spaces are defined using properties for the corresponding function spaces on the unit disk in the complex plane, and we show that, in general, different properties lead to different function spaces. We catalogue almost completely the various relationships between these spaces.     

关于弱MCP空间与弱层空间

本文引入了与已知的一些空间类非常类似的两个概念,我们分别称它们为弱MCP空间与弱层空间.本文主要讨论了这两空间类的等价命题与一些基本性质,及它们与原有空间类的关系.     

齐型空间上的Herz空间及其应用

定义了一类齐型空间上的Herz空间及弱Herz空间,研究了定义在这些空间中的一类次线性算子的性质．     

Quasi-Nagata空间的映射定理

本文讨论了quasi—Nagata空间与一类重要广义度量空间k—半分层空间的关系。证明了quasi—Nagata空间的一些映射性质。     

Some remarks on functions with values in probabilistic normed spaces

In this paper we consider an enlargement of the notion of the probabilistic normed space. For this new class of probabilistic normed spaces we give some topological properties. By using properties of the probabilistic norm we prove some differential and integral properties of functions with values into probabilistic normed spaces. As special cases, results for deterministic and random functions can be obtained.      

锥度量空间中的一些新的拓扑性质

本文给出了锥度量空间中的锥的一些性质.利用完备性概念,得到了此空间中的闭球套定理,改进了前人在度量空间中的相应结果.     

实值函数与某些覆盖性质

In the paper [properties defined with semi-continuous functions and some related spaces',Houston J.Math.,2015,41(3):1097–1106] properties(U L)~(wl)_m,(U L)~K_m and(U L)_m were defined and it was shown that spaces having these properties coincide with countably paracompact spaces,countably mesocompact spaces and countably metacompact spaces,respectively.In this paper,we continue with the study on the relationship between properties defined with real-valued functions and some covering properties.Some characterizations of countably compact spaces and pseudo-compact spaces in terms of real-valued functions are obtained.     

关于度量投影的连续性

本文引入的Ｂａｎａｃｈ空间的（Ｃ－Ｉ）、（Ｃ－Ⅱ），（Ｃ－Ⅲ）等几何性质，证明了如下结果。设Ｍ是Ｂａｎａｃｈ空间的逼近凸子集，如果Ｂａｎａｃｈ空间有性质（Ｃ－Ｉ），（Ｃ－Ⅱ）（Ｃ－Ⅲ），则度量投影ＰＭ连续（范数－范数上半连续，范数－弱上半连续）。这些结果推广了文（４，７，８）相应的定理。最近，Ｄ．Ｋｕｔｚａｒｏｖａ，Ｂｏｒ－Ｌｕｈ Ｌｉｎ等引入了一些新的凸性空间，本文还研究了这些凸性空间中度量投影     

关于sn-度量空间

本文利用ｓｎ－度量空间的一些等价刻划及ｓｎ－度量空间与ｇ－度量空间、度量空间之间的关系，研究了ｓｎ－度量空间的一些映射性质，证明了ｓｎ－度量空间的闭象是ｓｎ－度量空间当且仅当它是ｓｎ－第一可数的，利用这一结果证明了有限到一闭映射和开闭映射均保持ｓｎ－度量空间，并给出反例说明完备映射不保持ｓｎ－度量空间，本文还证明了ｓｎ－变量空问满足完备逆象Ｇδ－对角线定理．     

Fiberwise absolute neighborhood extensors for a class of metrizable spaces

In the paper we study fiberwise absolute neighborhood extensors with respect to some classes of metrizable spaces by means of the local extension properties and the lifting properties of the underlying spaces.     

ConvergenceLF spaces

In this paper we examineLF spaces, inductive limits of Fréchet spaces, in two different settings: the categoryCV S of convergence vector spaces and the categoryLC S of locally convex topological vector spaces. Special attention is given to permanence properties and retractivity properties in each case. Some interaction between properties ofLF spaces inCV S and other properties inLC S are investigated.R. Beattie's research was supported by NSERC grant OGP0005316.     

关于概率准度量族空间的等距同构

引入了带指标的准度量族空间的概念，讨论了带指标的准度族空间与概率准度量族空间和随机准度量族空间之间的关系，建立了这些空间的一些性质，研究了这些空间的等矩同构．     

鞅空间K（lnK）^q和M（lnM）^q（q〉0）的定义及性质

在鞅的研究中,人们把具有某种相同性质的鞅归为一类,这就形成了许多不同的鞅空间.本文定义了两组新的鞅空间,并给出了这两组鞅空间之间以及它们与已知鞅空间的关系,最后给出了这两组鞅空间的有关性质.     

Metric projections versus non-positive curvature

In this paper two metric properties on geodesic length spaces are introduced by means of the metric projection, studying their validity on Alexandrov and Busemann NPC spaces. In particular, we prove that both properties characterize the non-positivity of the sectional curvature on Riemannian manifolds. Further results are also established on reversible/non-reversible Finsler–Minkowski spaces.     

鞅空间K(lnK)~q和M(lnM)~q(q>0)的定义及性质

在鞅的研究中,人们把具有某种相同性质的鞅归为一类,这就形成了许多不同的鞅空间.本文定义了两组新的鞅空间,并给出了这两组鞅空间之间以及它们与已知鞅空间的关系,最后给出了这两组鞅空间的有关性质.     

Two new properties of ideals of polynomials and applications

In this paper we introduce two properties for ideals of polynomials between Banach spaces and showhow useful they are to deal with several a priori different problems. By investigating these properties we obtain, among other results, new polynomial characterizations of L_∞ spaces and characterizations of Banach spaces whose duals are isomorphic to f 1 (Λ).