关于具有与某集合有关的正则Gδ对角线的空间的注记

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 generalize the result in [1,2].