Abstract: This paper proves the following results：Let X ＝l σ,π,Λ} ,|Λ|= λ,and every pro-
jection πσ：X → Xσbe an open and onto mapping．（A）If X is  λ-paracompact and every X σis normal and δθ-refinable，then X is normal and  δθ-refinable；（B）If X is hereditarily  λ-paracompact and every X σis hereditarily normal and hereditarily  δθ-refinable， then X is hereditarily normal and hereditarily δθ-refiable .

Key words: inverse limit； λ-paracompact； normal and , δθ-refinable； hereditarily , normal； hereditarily δθ-refinable .