g—可度量空间的完备逆象

本文的主要目的是建立ｇ－可度量空间的两个映射定理：（１）ｇ－可度量空间是度量空间的商紧映象；（２）ｇ－可度量空间的完备逆象若具有Ｇδ－对角线，那么它是ｇ－可度量空间。     

关于( )-空间和g-可度量空间

本文利用序列覆盖分层强紧映射，建立了（ ）-空间，g-可度量空间与特定的度量空间的关系，这是对Alexandroff的部分问题的肯定回答。     

完备和紧度量空间中的不动点

利用实函数性质,建立了两类度量空间中的几个不动点定理,推广了Fisher的有关定理。     

有限测度诱导的度量空间的完备性

In this paper,the metric space(A, ρ） induced by finite measure space(X,A,μ） is introduced completeness and researched.     

关于k－半分层空间的度量化

本文将给出ｋ－半分层空间的若干度量化定理以及分层空间和σ－空间的度量化定理．     

具有对称的集合和完备度量空间上两个自映射的共同不动点

本文给出了具有对称的集合上两个自映射有唯一共同不动点的充要条件.同时,还给出了完备度量空间上两个自映射有共同唯一不动点的条件.     

完备序度量空间中的耦合公共点理论

本文通过构造特殊的映射和函数,利用压缩定理,研究完备序度量空间中耦合公共点的存在性和唯一性,改进了最近的一些结果.     

Hutchison度量完备的充要条件

距离空间Ｘ上，以Ｍ（Ｘ）记定义在Ｘ的Ｂｏｒｅｌ域上的具有有界支撑的概度测度全体，Ｒ（Ｘ）记Ｍ（Ｘ）中所有Ｒａｄｏｎ测度，Ｍ（Ｘ），Ｒ（Ｘ）均赋予Ｈｕｔｃｈｉｓｏｎ度量，本文得到：Ｒ（Ｘ）完备当且仅当Ｘ完备且有界，若Ｘ可分，则：Ｍ（Ｘ）完备当且仅当Ｘ完备且有界。     

Perfect Preimages of Some Spaces

ＰｅｒｆｅｃｔＰｒｅｉｍａｇｅｓｏｆＳｏｍｅＳｐａｃｅｓ￥（林寿）ＬｉｎＳｎｏｕ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｉｎｇｄｅＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ，Ｎｉｎｇｌｅ，Ｆｕｊｉｎａ，３５２１００）Ａｂｓｔｒａｃｔ：ＩｎｔｈｉｓＰ...     

Images and Preimages of D_0 Spaces

ＩｍａｇｅｓａｎｄＰｒｅｉｍａｇｅｓｏｆＤ_０Ｓｐａｃｅｓ￥ＤａｉＭｕｍｉｎ；ＣｈｅｎＨａｉｙａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈ．ａｎｄＩｎｆｏｒｍａｔｉｏｎＳｃｉｅｎｃｅ，ＵｎｉｖｅｒｓｉｔｙｏｆＧｕａｎｇｘｉ）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｐｅｐ?..     

On the Dimension of Preimages of Certain Paracompact Spaces

It is proved that if X is a normal space which admits a closed fiberwise strongly zero-dimensional continuous map onto a stratifiable space Y in a certain class (an S-space), then IndX = dimX. This equality also holds if Y is a paracompact σ-space and ind Y = 0. It is shown that any closed network of a closed interval or the real line is an S-network. A simple proof of the Kateˇ tov–Morita inequality for paracompact σ-spaces (and, hence, for stratifiable spaces) is given.     

关于完全仿紧空间的一些刻画

本文在Ｔ１正则的条件下得到了完全仿紧空间的一些等价刻画,并利用所得到的刻画证明了这类空间的一个可数乘积定理。     

A New Class of Perfect Fréchet Spaces

This paper deals with a new class of perfect Frèchet spaces which can be obtained by interpolation of echelon spaces: l_p,q[a_m,n]. We determine the reflexive, Montel, Schwartz, totally reflexive, totally Montel and nuclear spaces l_p,q[a_m,n]. We also derive results on closed subspaces on the spaces (l_p,q)(N).     

原像Occlusion运算的交换性

设a_γ=(a,γ)和b_δ=(b,δ)是两个原像,且b■a.通过集运算,得到a_γ和b_δ关于occlusion运算能交换的充要条件,特别得到在δ■γ的情形下aγ和bδ能交换的充要条件,并给出正反两方面的例子.     

Fuzzy Perfect Mappings and Q-Compactness in Smooth Fuzzy Topological Spaces

We point out that the product of two fuzzy closed sets of smooth fuzzy topological spaces need not be fuzzy closed with respect to the the existing notion of product smooth fuzzy topology. To get this property, we introduce a new suitable product smooth fuzzy topology. We investigate whether $F_1\times F_2$ and $(F,H)$ are weakly smooth fuzzy continuity whenever $F_1$, $F_2$, $F$ and $H$ are weakly smooth fuzzy continuous. Using this new product smooth fuzzy topology, we define smooth fuzzy perfect mapping and prove that composition of two smooth fuzzy perfect mappings is smooth fuzzy perfect under some additional conditions. We also introduce two new notions of compactness called $Q$-compactness and $Q$-$\alpha$-compactness; and discuss the compactness of the image of a $Q$-compact set ($Q$-$\alpha$-compact set) under a weakly smooth fuzzy continuous function ($(\alpha ,\beta )$-weakly smooth fuzzy continuous function).     

Minimal Number of Preimages Under Maps of Surfaces

We compute the minimal number of roots of the equation $f(x) = c$ for a map $f$ belonging to a given homotopy class of maps between closed (not necessarily oriented) surfaces.