This paper proves the following results: Le t X= lim ←｛X σ,π σ ρ,Λ｝,｜Λ｜=λ, and every p rojection π σ: X→X σ be an open and onto mapping. (A) If X is λ-paracompact and every X σ is normal and δθ-ref...This paper proves the following results: Le t X= lim ←｛X σ,π σ ρ,Λ｝,｜Λ｜=λ, and every p rojection π σ: X→X σ be an open and onto mapping. (A) If X is λ-paracompact and every X σ is normal and δθ-refinable, then X is normal and δθ-refinable; (B) If X is hereditarily λ-pa racompact and every X σ is hereditarily normal and hereditarily δθ- refinable, then X is hereditarily normal and hereditarily δθ-refiable .展开更多
In this paper, the hereditarily almost expandability of inverse limits is investigated, with two results obtained. Let X be the inverse limit space of an inverse system （Xα, π^αβ, ∧}. （1） Suppose X is heredita...In this paper, the hereditarily almost expandability of inverse limits is investigated, with two results obtained. Let X be the inverse limit space of an inverse system （Xα, π^αβ, ∧}. （1） Suppose X is hereditarily κ-metacompact, if each Xα is hereditarily pointwise collectionwise normal （almost θ-expandable, almost discrete θ-expandable）, then so is X; （2） Suppose X is hereditarily κ-σ-metacompact, if each Xα is hereditarily almost σ-expandable （almost discrete σ-expandable = σ-pointwise collectionwise normal）, then so is X.展开更多
文摘This paper proves the following results: Le t X= lim ←｛X σ,π σ ρ,Λ｝,｜Λ｜=λ, and every p rojection π σ: X→X σ be an open and onto mapping. (A) If X is λ-paracompact and every X σ is normal and δθ-refinable, then X is normal and δθ-refinable; (B) If X is hereditarily λ-pa racompact and every X σ is hereditarily normal and hereditarily δθ- refinable, then X is hereditarily normal and hereditarily δθ-refiable .
基金Supported by the Scientific Fund of the Educational Committee of Xinjiang of China (XJEDU2004158)
文摘In this paper, the hereditarily almost expandability of inverse limits is investigated, with two results obtained. Let X be the inverse limit space of an inverse system （Xα, π^αβ, ∧}. （1） Suppose X is hereditarily κ-metacompact, if each Xα is hereditarily pointwise collectionwise normal （almost θ-expandable, almost discrete θ-expandable）, then so is X; （2） Suppose X is hereditarily κ-σ-metacompact, if each Xα is hereditarily almost σ-expandable （almost discrete σ-expandable = σ-pointwise collectionwise normal）, then so is X.
