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 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.
