In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fσ-subspaces. For a generalized ordered （GO）-space X, we also show that X is mon...In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fσ-subspaces. For a generalized ordered （GO）-space X, we also show that X is monotonically metacompact if and only if its closed linearly ordered extension X＊ is monotonically metacompact. We also point out that every non-Archimedean space X is monotonically ultraparacompact. In the second part of this note, we give an alternate proof of the result that McAuley space is paracompact and metacompact.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
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
基金Supported by the National Natural Science Foundation of China(Grant No.11271036)Beijing Natural Science Foundation(Grant No.1102002)Doctoral Fund of Innovation of Beijing University of Technology
文摘In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fσ-subspaces. For a generalized ordered （GO）-space X, we also show that X is monotonically metacompact if and only if its closed linearly ordered extension X＊ is monotonically metacompact. We also point out that every non-Archimedean space X is monotonically ultraparacompact. In the second part of this note, we give an alternate proof of the result that McAuley space is paracompact and metacompact.
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.
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Partially supported by Beijing Municipal Bureau of Personnel of China(No.005400703)Institute of Mathematics and Interdisciplinary Science,Capital Normal University.
