摘要
设P(X)是集合X的非空子集全体按集合的包含关系作成的半序集,A:P(X)→P(X)是增算子.X上的实泛函族{Tλ|λ∈A}称为是A型的,如果对任伺满足的子集E(X)都有得到了A型泛函族的共鸣定理定理1拓扑空间X的每个点点上方有界的A型泛函族都在X的某相应的非空开集上一致上方有界的充要条件是:X的任何满足条件的非空子集列都至少有一个元的内部非空.
Let P(X)be the Partially ordered space of all nonempty subests of set X under the containing relation of sets. A real functiods{Tλ|λ∈A}is taled to be of A-type if sup{Tλ(x)|λ∈A,x∈A(E)}<+∞for every subest E whixch satisfies the conditionsup{Tλ(x)|∈A, x∈E} <+∞The resonance theorem of the functionals of A-atype is obtained.Theorem 1 Every pointwise upper bounded functionals of A-type on X is uniformly upper bounded in some nonempty open set,if and only if every nonempty subest sequence {Xn} which satisfies the conditionhas at least one element with nonempty interior
出处
《西南师范大学学报(自然科学版)》
CAS
CSCD
1996年第1期14-17,共4页
Journal of Southwest China Normal University(Natural Science Edition)
关键词
A型泛函数
A型空间
增算子
共鸣定理
functionals of A-type
space of A-type
pointwise upper bounded
uniformly upper bounded
increasing operator
Z_F space