关于具有与某集合有关的正则G_δ对角线的空间的注记(英文)  

A NOTE ON SPACES WITH A REGULAR G_δ -DIAGONAL RELATED TO A SET

作　　者：李竞[1] 彭良雪[1] 

机构地区：[1]北京工业大学应用数理学院,北京100124

出　　处：《数学杂志》2013年第4期603-608,共6页Journal of Mathematics

基　　金：Supported by Beijing Natural Science Foundation(1102002);he National Natural Science Foundation of China(11271036)

摘　　要：本文研究了空间X中具有一定性质的子集可度量化的问题.利用一般拓扑学证明一个空间可度量的方法,得到如下结论:若正则空间具有与其有界子集有关的正则Gδ对角线,那么该子集的闭包是可度量化的;若正则空间具有与其有界强零集A有关的Gδ对角线,那么该子集A是X的紧可度量的子空间,推广了文献[1,2]的结果.In this note, we study a problem that when the subset A of a space X is metrizable. By the usual methods of proving a space to be metrizable in general topology, we get the following conclusions： we show that if a set A is a bounded subset of a regular space X and X has a regular Gδ-diagonal related to a set A, then A is metrizable. And we get that if F is a bounded strong zero-set of a regular space X and X has a regular Gδ-diagonal related to the set F, then F is a compact metrizable subspace of X, which ueneralize the result in [1. 2].

关 键 词：正则Gδ对角线 可度量化 强零集 

分 类 号：O189.1[理学—数学]