遗传$sigma$-亚紧空间及其乘积.doc

,,1998σ-(643000)σ-σ-TychonoffTychonoffσ-σ-σ-MR(1991)σ-σ-σ-Tychonoff54E18,-pactSpaceandItsProductPropertiesZhuPeiyong(DepartmentofMathematics,ZigongTeachers’College,Zigong643000,China)AbstractInthispaper,wefirstproveagroupofequivalentcharacterizationsofheredi-tarilyσ--,weshowthattheaboveTychononoffproducttheoremsdonotholdifhereditarilyσ-pactisreplacedbyσ--pact,Scatteredpartition,σ-pointfiniteopenex-pansion,σ-pointfiniteopenrefinement,Tychonoffproduct,σ-product1991MRSubjectClassification54E18,[1]σ-(A)Xσ-Yσ-σ-X×YXσ-(B)X=i<ωXi∀n<ω,i<nXiσ-1996-03-15,1997-02-03,1997-10-1353241(C)X=σ{Xα:α∈A},Xσ-Xσ-σ-x(A)(B)X,YU|Y,(U)xN(x){U∩Y:∅U∈U},{U∈U:x∈U}ωα,β,γ,δ¯|A|AAA[A]n={σ⊂A:|σ|=n}[A]<ω=∪[A]∈[1,2](scatteredpartition)X{Lα:α<γ}∀β<γ,∪{Lα:α<β}=∪Vnn∈ωUσ-VX(1)Vn(2)∪V=∪=∪Vnn∈ω∀n∈ω,Vn={Vαn:α<γ},V{Fα:α<γ}σ-Vn∀α<γFα⊂∪∈-σ--{Xα:α∈A}σ-{Xα:α∈A}∀x=(xα)α∈Aσ{Xα:α∈A}={x=(xα)α∈A∈{Xα:α∈A}:|Q(x)|<ω}.{Xα:α∈A}Tychonoffs=(sα)α∈A∈{Xα:α∈A},Q(x)={α∈A:xα=sα}.σ{Xα:α∈A}{Xα:α∈A}σ-sσ{Xα:α∈A}{Xα:α∈a}σ-∀α∈[A]<ω,Tychonoff2σ--Xσ-γ},∗{Fα:α<γ}⊂{Fα:α≤γ}∗{Fα:α<γ},{Fα:α≤δ<γ,Fδ=∩α<,(1)X(2)X(3)X(4)Xσ-σ-{Fα:α<γ}{Uα:α<γ}σ-σ-V=∪Vnn∈ω∀α<γ,X−Fα=∪{