σ-集体正规与σ-满正规的可数乘积

On Countable Products of σ-Collectionwise Normality and σ-Fully Normality

在逆序列的情形下,假设极限空间是可数仿紧时.证明了σ-集体正规性、σ-满正规性可被其极限空间保持,同时证明了遗传σ-集体正规性、遗传σ-满正规性在无需对极限空间X附加任何条件的情况下可被其逆极限空间保持.利用这两个结果,分别得到了相关的两个具有可数个无限因子的Tychonoff乘积定理.

It proves that in the case of inverse sequence,theσ-collectionwise,σ-fully normality can be pre-served by the inverse limit spaces under the usually assumption of countable paracompactness.Further-more it also shows the the corresponding hereditarily properties can be preserved by the inverse limit spaces even without any assumption of the projections and the inverse limit spaces.As some applications, two theorems about countable Tychonoff product properties have been given.