摘要
在集论ZF+DC中,我们给出了强Z-拟连续偏序集P到单位闭区间[o,1]的Z-态射的一个直接的构造法,证明了p到[o,1]的Z-态射全体强分离P中的点.该文引入了Z-完备偏序集P的权ω(P)和p的Z-嵌入基数λ_z(P),证明了:(1)若P为完备格,λ_z(P)>0,则ω(P)≤max{ω,λ_z(P)};(2)若尸为强Z-拟连续偏序集,则0<λ_z(P)≤ω(P)^(2);(3)若p为强Z-拟连续偏序集,ω(P)≤ω,则p可用保任意交与Z-并映射(简称为IZ^(+)-映射)嵌入到Hilbert方体[o,1]_(?)之中.若进一步P为完备格,则反之也成立.
: In the theory ZF+DC ,we present a direct approach to the construction of Z-morphisms ofstrongly Z-precontinuous posets,a generalization of continuous posets,into the unit interval,and show that astrongly Z-precontinuous poset has sufficiently many Z-morphisms into the unit interval to strongly separatethe points. In this paper, the weight w(P) and Z-embedding cardinal (P) of a Z-complete poset P are intro-duced. We prove that (1) lf P is complete and (P)>0, then w(P)≤max { (P) },and (2) If P is strong-Iy Z-precontinuous, then 0< (P)≤w(P)2.
出处
《江西师范大学学报（自然科学版）》
CAS
1995年第1期12-22,共11页
Journal of Jiangxi Normal University(Natural Science Edition)
基金
国家数学天元基金
国家青年自然科学基金
江西省自然科学基金资助项目
关键词
Z-below关系
Z-拟连续偏序集
权
Z-嵌入基数
: Z-below relation, (strong) Z-precontinuity,Z-morphism,weight of a poset,embedding,Z-embedding cardinal of a Z-complete poset
