摘要： 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 .
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