集体次正规空间的逆极限与无限Tychonoff积

Inverse limits and infinite tychonoff products about collectionwise subnormal spaces

主要证明:(1)并且每个是开满映射,如果X是|∑|-完满的且每个Xσ是集体次正规空间,则X是集体次正规空间．(2)如果是|A|-完满正规的,则X是集体次正规空间当且仅当是集体次正规的．同时指出:遗传集体次正规也有相应的性质．

This paper mainly proves the results:(1)Let X=and every π_σ. be open andonto mapping, if X is norma|Σ|-paracompact and every X_σ is collectionwise subnormal, then X iscollectionwise subnormal;(2)Let X=Π_(αeA)X-α is normal|A|-paracompact,X is collectionwise subnormalif Π_(αeσ)X-α is collectionwise subnormal for every σ∈[A]]. Next, we point out that there exist thesimilar results to hereditarily collectionwise subnormal spaces.