关于遗传超仿紧空间的Tychonoff乘积性质

On the Tychonoff product property of hereditarily ultraparacompact space

本文主要证明:(1)如果X=Πσ∈ΣXσ是遗传|Σ|-超仿紧空间,则X是遗传超仿紧空间当且仅当F∈Σ,Πσ∈FXσ是遗传超仿紧空间.(2)设X=Πσ∈ΣXσ是遗传可数超仿紧空间,则下列三条等价:X是遗传超仿紧空间;F∈[ω]<ω,Πi∈FXi是遗传超仿紧空间;n∈ω,Πi≤nXi是遗传超仿紧空间.

This paper obtains the following conclusions： （1） let X =∏σ∈∑Xσ be hereditarily ｜∑｜-ultraparacompact space, then X is hereditarily ultraparacompact space if ∏σ∈FXσ is hereditarily ultraparacompact space for every F∈∑^〈w; （2） Let X=∏σ∈∑Xσ be hereditarily coun-table ultraparacompact, then the followings are equivalent： S is hereditarily ultraparacompact space; А↓F∈[ω]^〈ω,∏i∈FXi is hereditarily ultraparacompact space; ∏isnXiis hereditarily ultrapar-acompact space for each n ∈ ω.