弱次亚紧空间和遗传弱次亚紧空间的逆极限

On Inverse Limits Proposition of Normal Weakly Subme Tacompate Spaces

证明了 :若X =lim← {Xσ,πσρ,Λ} ,|Λ|=λ ,并且每个映射πσ:XXσ 是开满射 ,那么若X是λ 仿紧的 ,并且每个Xσ 是正规弱次亚紧空间 ,则X是正规弱次亚紧空间 .进一步还得到了遗传正规的遗传弱次亚紧性的类似结果 .

The following resutls are proved: Assume that X= lim ←｛x\-σ, π σ ρ, Λ｝, ｜Λ｜=λ , and the projection π σ: XX\-σ is an open and onto mapping for every σ∈Λ , if X is λ -Paracompact and every X\-σ is normal and weakly submetacompact, the X is normal and weakly submetacompact. Moreover, an analogous result of hereditarily normal weakly submetacompact is obtained.