正规弱-可加细空间的无限乘积

Infinite Products of Weakly -Refinable Normal Spaces

主要证明了如下结果 :(1)如果是X =∏σ∈ Xσ 是 | |-仿紧空间 ,则X是正规弱θ -可加细空间当且仅当 F∈ [ ]<ω,∏σ∈FXσ 是正规弱θ -可加细空间 .(2 )设X =∏i∈ωXi 是可数仿紧的 ,则下列 3条等价 :X是正规弱θ -可加细的 ; F∈ [ω]<ω,∏i∈FXi 是正规弱θ -可加细的 ; n∈ω ,∏i≤nXi 是正规弱θ -可加细的 .

This paper mainly proves following : (1) Let X=∏ σ∈ X σ be ||-paracompact,X is normal weak θ-refinable iff ∏ σ∈ X σ is normal weak θ-refinable for every F∈|| <ω .(2)Let X=∏ i∈ω X i is countable paracompact, then the following are equivalent:X is normal weak θ-refinable;F∈ <ω ,∏ σ∈F X σ is normal weak θ-refinable;n∈ω,∏ i≤n X i is normal weak θ-refinable.