首页 | 本学科首页   官方微博 | 高级检索  
     检索      

单调空间与度量化定理
引用本文:彭良雪,林寿.单调空间与度量化定理[J].数学学报,2003,46(6):1225-123.
作者姓名:彭良雪  林寿
作者单位:1. 北京工业大学应用数理学院,北京,100022
2. 福建师范大学数学系,福州,350007
基金项目:国家自然科学基金资助项目(10271026)
摘    要:本文回答了关于MCM空间遗传性的一个问题,讨论了k-MCM空间是k半层空间的条件,得到了一些用g函数刻划的度量化定理.主要结论有:MCM空间是关于Fσ子空间遗传的;在正规空间类中,q空间(ωN空间,k-MCM空间)是关于开Fσ子空间遗传的;如果X是具有Gδ对角线的正则次中紧 k-MCM空间,则X是k半层空间;X是可度量化空间的充要条件是存在X上的g函数满足对X中任意不相交的闭集F与紧集C,都有某个n∈ω,使得(∪x∈F g(n,x))∩(∪y∈C g(n,y))=(?).

关 键 词:MCM空间  k-MCM空间  q空间
文章编号:0583-1431(2003)06-1225-08
修稿时间:2001年11月21

On Monotone Spaces and Metrization Theorems
Liang Xue PENG.On Monotone Spaces and Metrization Theorems[J].Acta Mathematica Sinica,2003,46(6):1225-123.
Authors:Liang Xue PENG
Institution:Liang Xue PENG (College of Applied Science, Beijing University of Technology, Beijing 100022, P. R. China) (E-mail: lxuepeng@263.net.cn) Shou LIN (Department of Mathematics, Fujian Normai University, Fuzhou 350007, P. R. China) (E-mail: linshou@public.ndptt.fj.cn)
Abstract:In this paper an open problem about the hereditary of MCM-spaces is an-swered affirmatively, the condition which k-MCM-spaces are k-semistratifiable spaces is discussed, and some metrizable theorems are obtained by g-functions. The main results are that MCM-spaces are hereditary with respect to Fσ-subspaces; q-spaces(ωN-spaces, k-MCM-spaces) are hereditary with respect to open and Fσ-subspaces in normal spaces; a regular submesocompact k-MCM-space with a Gδ-diagonal is k-semistratifiable; and a space X is metrizable if and only if there is a g-function on X such that for any closed set F and compact set C in X, if
Keywords:MCM-spaces  k-MCM-spaces  q-spaces
本文献已被 CNKI 维普 万方数据 等数据库收录!
点击此处可从《数学学报》浏览原始摘要信息
点击此处可从《数学学报》下载免费的PDF全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号