伪概率度量空间

本文讨论了伪概率度量空间的拓扑性质,讨论了伪Menger空间的某种等价关系上的分划及等价类的度量性质。     

连通度量空间的映象

拓扑空间X称为s连通,若X不能表示为两个非空的不相交的序列开集之并.本文纠正了A.Fedeli和A.Le Donne关于连通度量空间映象的错误论证,证明了s连通性可刻画为连通度量空间的连续的序列覆盖映象,从而导出连通的序列空间(或Frechet空间)可刻画为连通度量空间的商映象(或伪开映象),回答了V.V.Tkachuk在Proc.Amer.Math.Soc.上提出的问题.     

连通度量空间的映象

拓扑空间X称为s连通,若X不能表示为两个非空的不相交的序列开集之并.本文纠正了A.Fedeli 和A.Le Donne关于连通度量空间映象的错误论证,证明了s连通性可刻画为连通度量空间的连续的序列覆盖映象,从而导出连通的序列空间(或FrEchet空间)可刻画为连通度量空间的商映象(或伪开映象),回答了V.V.Tkachuk在Proc.Amer.Math Soc.上提出的问题.     

模糊偏伪度量的表现定理及应用

本文借助概率分布函数的点式运算研究了模糊偏伪度量的表现定理,证明了由模糊偏伪度量空间(X,P,*)导出的右连续的映射族{pt}t∈(0,1)都是偏伪度量当且仅当(X,P,∧)也是模糊偏伪度量空间,进一步研究了此表现定理导出的模糊化拓扑空间。     

Erceg-度量的进一步简化及其性质

本文对Erceg-伪度量做了进一步简化,指出了史福贵的点式伪度量和Erceg-伪度量间的关系,并给出了Erceg-伪度量的一些性质.     

概率逻辑伪度量空间及其性质

论证有限多个公式的概率分布与生成它的原子公式集的概率分布之间的关系,然后把计量逻辑学与概率逻辑学相结合,提出了概率真度、概率逻辑伪度量空间(F(n),ρP);指出当取均匀概率分布时,概率真度就转化为计量逻辑学中的真度,同时两公式间的概率逻辑伪距离Pρ就转化为计量逻辑学中的伪距离ρ.从而在有限理论中建立了一种更具一般性的概率逻辑伪度量空间理论。     

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。     

三值R_0命题逻辑系统中理论的随机发散度

在三值R_0命题逻辑系统中,给出了随机相似度和随机逻辑伪距离的基本性质.然后在随机逻辑度量空间中提出了理论的随机发散度,指出全体原子公式之集在随机逻辑度量空间中未必是全发散的,其是否全发散取决于给定的随机数序的分布.     

KM伪度量空间中的模糊化收敛结构

分别提供了由KM伪度量到模糊化收敛结构和由模糊伪度量链到模糊化收敛结构的转化方法,并且证明了由KM伪度量诱导的模糊化拓扑进而诱导的模糊化收敛结构和KM伪度量直接诱导的模糊化收敛结构相同.而且,还证明了由KM伪度量诱导的模糊伪度量链进而诱导的模糊化收敛结构和由KM伪度量直接诱导的模糊化收敛结构相同.     

Banach空间闭超平面上度量投影的连续性

该文给出Banach空间X的对偶空间X~*中闭超平面上度量投影的表达式,并在Banach空间中研究了闭超平面上度量投影的连续性.     

局部强紧空间的Hoare空间与Smyth空间

本文主要讨论局部强紧空间的性质,特别是其Hoare空间和Smyth空间的性质,证明了T_0空间为局部强紧空间的当且仅当其Hoare空间为局部强紧空间,局部强紧空间的Smyth空间为C-空间.对于强局部紧空间,我们有类似的结论.     

On the properties of topological entropy on a compact family of maps

The properties of topological entropy as a function on a compact family of maps of a compact metric space are studied.     

Functor of Extension of Contractions on Urysohn Universal Spaces

The aim of the paper is to show that there exists a functor of extension of contractions (i.e. nonexpansive maps) between compact subsets of a bounded Urysohn space (see Definition 2.1) to contractions acting on the whole space. The analogous result for the category of isometries between compact subsets of the unbounded Urysohn space is proved. Special properties of the functors are established.     

On dual locally uniformly rotund norms

We show that the existence of an equivalent dual LUR norm on a dual Banach space can be characterized by a topological property similar to the fragmentability. The compact spaces homeomorphic to weak* compact subsets of a dual LUR Banach space have the same properties as the class of Radon-Nikodym compact spaces. Research supported by the DGICYT PB 95-1025.     

R_0代数中素滤子的拓扑性质

首先讨论了R_0代数M中MP滤子、素滤子的基本性质,然后通过自然的方式在M的全体素滤子之集PF_(IL)(M)上构造拓扑,证明了PF_(IL)(M)是紧致的T_0空间.最后把PF_(IL)(M)上的拓扑限制在M的全体极大滤子之集MF_(IL)(M)上,得到MF_(IL)(M)是紧致的Hausdorff空间.     

Coburn Type Operators and Compact Perturbations

A bounded linear operator T acting on a Hilbert space is called Coburn operator if ker(T ? λ) = {0} or ker(T ? λ)^*= {0} for each λ ∈ C. In this paper, the authors define other Coburn type properties for Hilbert space operators and investigate the compact perturbations of operators with Coburn type properties. They characterize those operators for which has arbitrarily small compact perturbation to have some fixed Coburn property.Moreover, they study the stability of these properties under small compact perturbations.     

A MACHINE PRODUCING NON-*LINDELOF SPACES

The authors construct a machine putting out non-*Lindelof spaces, prove that many interesting topological properties can be preserved after the process, and with the aid of this machine obtain an example of locally compact, ccc, non-*Lindelof space and a consistent example of first countable, locally compact, ccc, non-*Lindelof space.     

Spaces of idempotent measures of compact metric spaces

We investigate certain geometric properties of the spaces of idempotent measures. In particular, we prove that the space of idempotent measures on an infinite compact metric space is homeomorphic to the Hilbert cube.     

仿紧空间和S-闭空间的共同推广

定义了仿S紧空间的概念,它是仿紧空间和S－闭空间的共同推广,文中讨论了仿S紧密空间的一些性质,推广了仿紧空间和S－闭空间的部分结果。     

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.