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
In this paper,we present that if Y is a hereditarily metacompact space and{Xn：n∈ω}is a countable collection of Cech-scattered metacompact spaces,then the followings are∏equivalent：（1）Y×∏n∈ωXn is metacom...In this paper,we present that if Y is a hereditarily metacompact space and{Xn：n∈ω}is a countable collection of Cech-scattered metacompact spaces,then the followings are∏equivalent：（1）Y×∏n∈ωXn is metacompact,（2）Y×∏n∈ωXn is countable metacompact,（3）Y×n∈ωXn is orthocompact.Thereby,this result generalizes Theorem 5.4 in[Tanaka,Tsukuba.J.Math.,1993,17：565–587].In addition,we obtain that if Y is a hereditarilyσ-metacompact space and{Xn：n∈ω∏}is a countable collection of Cech-scatteredσ-metacompact spaces,then the product Y×n∈ωXn isσ-metacompact.展开更多
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.
基金Supported by the Scientific Research Fund of Sichuan Provincial Education Department(Grant No.14ZB0007)
文摘In this paper,we present that if Y is a hereditarily metacompact space and{Xn：n∈ω}is a countable collection of Cech-scattered metacompact spaces,then the followings are∏equivalent：（1）Y×∏n∈ωXn is metacompact,（2）Y×∏n∈ωXn is countable metacompact,（3）Y×n∈ωXn is orthocompact.Thereby,this result generalizes Theorem 5.4 in[Tanaka,Tsukuba.J.Math.,1993,17：565–587].In addition,we obtain that if Y is a hereditarilyσ-metacompact space and{Xn：n∈ω∏}is a countable collection of Cech-scatteredσ-metacompact spaces,then the product Y×n∈ωXn isσ-metacompact.
