正规弱次亚紧空间Tychonoff乘积的刻画

Tychonoff product characterizations of normal weak submetacompact spaces

文章主要证明了如下结果:(1)如果X=∏α∈Λ的当且仅当F∈[Λ]<ω,∏α∈FXα是正规弱次亚紧的;(2)如果X=i∈∏ωXi是可数仿紧的,则下列三条等价:X是正规弱次亚紧的;F∈[ω]<ω,∏i∈FXi是正规弱次亚紧的;n∈ω,i≤∏nXi是正规Xα是|Λ|仿紧空间,则X是正规弱次亚紧弱次亚紧的。

This paper mainly proves the following results, （1） Let X = ∏a∈AXa be ｜A｜ - paracompact, X is normal weak submetacompact, if ∏a∈FXa is normal weak submetacompact for every F ∈[A]^〈w.（2） Let X = ∏i∈wXi is countable paracompact, then, the following three are equivalent. X is normal weak submetacompact for every F ∈[A]^〈w;∨F ∈[w]^〈w, ∏i∈FXi is normal weak submetacompact;∨n∈w, ∏i≤nXi is normal weak submetacompact .