可缩空间的乘积性

The Multiplycation of Shrinked Space

主要证明了如下几个结果 :1.设X =Πσ∈ΣXσ是｜Σ｜ 仿紧空间 ,则X是可缩的 (具有B性质 ,D性质 )当且仅当 F∈ [Σ]<ω,Πσ∈FXσ 是可缩的 (具有B性质 ,D性质 ) ;2 .设X=Πi∈ωXi可数仿紧 ,则下面各条等价 :(1)X是可缩的 (具有B性质 ,D性质 ) ;(2 ) α∈ [ω]<ω,Πi∈αXi是可缩的 (具有B性质 ,D性质 ) ;(3) n ∈ω ,Πi<nXi 是可缩的 (具有B性质 ,D性质 )

The following results are proved:1.if X=Πσ∈ΣX σ is |Σ|paracompact,then X is shrinked(with B property or with D property) iff Πσ∈FX σ is shrinked (with B property or with D property) for  F∈[Σ] <ω ;2.if X=Πi∈ωX i is countable paracompact,then the following is equivelent each other: (1)X is shrinked (with B property or with D property); (2)Πi∈αX i is shrinked (with B property or with D property) for α∈[ω] <ω ; (3)Πi<nX i is shrinked (with B property or with D property) for n∈ ω.