正规弱δθ-可加空间的逆极限

THE INVERSE LIMFTS OF NORMAL WEAKLY δθ- REFINABLE SPACES

本文证明了如下结果:设X=lim←狖Xs,pr ,∧狚,|∧|=l ,并且每个投射ps:X→Xs是开满射,(a).若X是l-仿紧的并且每个Xs是正规弱dq-可加空间, 则X是正规弱dq-可加空间;(b).若X是l-仿紧的并且每个Xs是遗传正规的遗传弱dq-可加空间, 则X是遗传正规的遗传弱dq-可加空间.

This paper proves the following results:Let X={Xs , p, ∧}, |∧|=l ,and every ps : X→Xs be open and ontomapping ,(1)if X is l-paracompact and every Xs is normal and weakly dq-refinable, then X is normal and weakly dq-refinable; (2) if X is hereditarily l-paracompact and every Xs is hereditarily normal and hereditarily weakly dq-refinable, then X is hereditarily normal and hereditarily weakly dq -refinable;