正规弱θ-可加空间的逆极限性质

The inverse limits proposition of normal weakly θ-refinable spaces

本文证明了如下结果 :设 X=lim← {Xσ,πσρ,∧ },|∧ |=λ,并且每个投射 πσ:X→ Xσ是开满射 ,( 1 )若 X是λ仿紧的并且每个 Xσ是正规弱θ可加细空间 ,则 X是正规弱θ可加细空间 .( 2 )若 X是λ仿紧的并且每个 Xσ是遗传正规的遗传弱 θ 可加细空间 ,则 X是遗传正规的遗传弱 θ 可加细空间 .

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