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 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
It is proved in this paper that(1) the topological sum of a family of supercomplete spaces is supercomplete;(2) if X is a metacompact and almost locally compact space then X is supercomplete. Moreover, some questions ...It is proved in this paper that(1) the topological sum of a family of supercomplete spaces is supercomplete;(2) if X is a metacompact and almost locally compact space then X is supercomplete. Moreover, some questions on supercomplete spaces are posed in the paper.展开更多
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 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 National Natural Science Foundation of China(11201414,11571158,11171162)Supported by the Natural Science Foundation of Fujian Province(2012J05013)Supported by the Training Programme Foundation for Excellent Youth Researching Talents of Fujian's Universities(JA13190)
文摘It is proved in this paper that(1) the topological sum of a family of supercomplete spaces is supercomplete;(2) if X is a metacompact and almost locally compact space then X is supercomplete. Moreover, some questions on supercomplete spaces are posed in the paper.
