弱-可加空间的逆极限

Inverse Limits in Weakly -refinable Spaces

证明了两个结果 :设X=lim←{Xσ,πσρ,Σ}并且每个πσ 是开满映射 ,(1)如果X是｜Σ｜ 仿紧的且每个Xσ 是正规弱 θ 可加的 ,则X是正规弱 θ 可加的 ;(2 )如果X是遗传 ｜Σ｜ 仿紧的且每个Xσ 是遗传正规的遗传弱 θ 可加空间 ,则X是遗传正规的遗传弱 θ

This paper proves the following results:let X= lim ←{X σ,π σ ρ,Σ} and every π σ be open and onto mapping, (1) if X is |Σ| paracompact and every X σ is normal and weakly refinable, then X is normal and weakly refinable; (2) if X is hereditarily |Σ| paracompact and every X σ is hereditarily normal and hereditarily weakly refinable, then X is hereditarily normal and hereditarily weakly refinable.