σ-集体正规空间的无限乘积性质

Infinite Prdouct Properity of σ-collectionwise Normal Spaces

证明了如下结果:(1)如果X=∏τ∈∑Xτ是λ-超仿紧空间,则X是σ-集体正规空间当且仅当F∈∑<ω,X=∏τ∈∑Xτ是σ-集体正规空间。(2)设X=∏i∈ωXi是可数仿紧的,则下列三条等价:X是σ-集体正规的;F∈[ω]<ω,X=∏i∈FXi是σ-集体正规的;n∈ω,∏i≤nXi是σ-集体正规的。

The following are proved ： （ 1 ） Let X=∏τ∈∑Xτ be ｜λ｜-superparacompact, then X is σ- collectionwise normal spaces if only every F∈[∑]〈ω,X=∏τ∈∑Xτ is σ-collectionwise normal spaces. （2）Let X=∏i∈ωXi be countable paraeompaet , then the following are equivalent ： X is σ- collectionwise normal ; for every F∈[ω]〈ω,X=X=∏i∈ωXi is σ- collectionwise normal ; for every n∈ω,∏i≤n Xi is σ- collectionwise normal.