内P-集合副集的σ-生成和σ-强生成

于秀清,董化玲,徐凤生

(德州学院 数学系,山东 德州 253023)

0 引言与预备知识

αF=α∪{α′|βα,f(β)=α′∈α,f∈F},

(1)

(2)

这里:β∈V,βα;f∈F把β变成f(β)=α′∈α.

(3)

则称XF是X生成的外P-集合(outer P-setXF),简称XF是外P-集合,且

XF=X∪{u|u∈U,uX,f(u)=x′∈X,f∈F},

(4)

1 内P-集合副集的σ-生成和σ-强生成

定义2如果

(5)

(6)

(7)

由定义1和定义2,可得如下结论.

Ø.

由定理3知: 对于∀σ*∈(σ1,σ2],

所以

Ø,

于是

(8)

(9)

(10)

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