摘要：本文研究了空間X中具有一定性質的子集可度量化的問題.利用一般拓撲學證明一個空間可度量的方法,得到如下結論:若正則空間具有與其有界子集有關的正則Gδ對角線,那么該子集的閉包是可度量化的；若正則空間具有與其有界強零集A有關的Gδ對角線,那么該子集A是X的緊可度量的子空間,推廣了文獻[1,2]的結果.%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].
