遗传正规弱-空间的无限乘积

Infinite tychonoff products of hereditarily weakly-refinable spaces

主要证明:(1)如果X=Πσ∈∑Xσ是遗传|∑|-仿紧空间,则X是遗传正规弱(?)-可加空间当且仅当(?)F∈|∑|<ω,Πσ∈FXσ是遗传正规弱(?)-可加空间.(2)设X=Πi∈ωXi是遗传可数仿紧的,则下列三条件等价:X是遗传正规弱(?)-可加的;(?)F∈[ω]<ω,Πi∈FXi是遗传正规弱(?)-可加的;(?)n∈ω,Πi≤nXi是遗传正规弱(?)-可加的.

This paper mainly proves: (1) Let X =Πσ∈∑Xσ be hereditarily |∑| -paracompact, X is hereditarily normal weak θ -refutable if Πσ∈∑Xσ is hereditarily normal weak θ -refinable for every F ∈ [∑]<ω. (2) LetX =Πi∈ωXi be hereditarily countable paracompact, then the following are equivalent: X is hereditarily normal weak θ -refinable; Πσ∈FXσ is hereditarily normal weak θ -refinable for each F ∈ [∑]<ω ;ΠisnXi is hereditarily normal weak θ -refinable for each n∈ω.