σ-满正规空间的逆极限

本文证明:设X是逆系统(X_απ_β~α,A}的逆极限,|A|=λ,假设每个投射π_α:X→X_α是开且到上的。X是λ-仿紧和λ-可遮的,如果每个X_α是σ-满正规的(可遮的,σ-集体正规的),则X是σ-满正规的(可造的,σ-集体正规的)。作为这一结果的推论,我们还将证明正规σ-满正规性满足如文[1]中的通常形式的逆极限定理及遗传σ-满正规性的类似结果。

Inverse Limit of σ-Fully Normal Spaces

In this paper, we shall prove the following theorem: Let X be the inverselimit of an inverse system {X_α,π_β~α, } and || = λ. Suppose that each projeetionπ_α: X→X_α is an open and onto map and X is λ-paracompact and λ-Screenable. Ifeach X_α is σ-fully normal (resp., screenab1e, σ-collectionwise normal), then X is σ-fullnormal (resp., screenable, σ-collectionwise normal). As a corollary of the result thenormal σ-fully normality satisfies the inverse limit theorem in the usual type as in [1].Moreover, we shall obtain the anologous result for hereditarily σ-fully normality.