集值映射空间上的Fréchet性质

摘要

It is shown by mean of k-sequences that continuous multifunction space Ck( X) is a Fréchet space if andonly if (iff) each open k-cover U of X contains a k-sequence. It is proven that Cωk(x) is a strict Fréchet space iffCk(X) is a Fréchet space (a strict Fréchet space, a strong Fréchet space, respectively) iff for each sequence {Un}n∈N of open k-covers of X, there is Un∈Un such that { Un }n∈N is a k-sequence of X. These generalize some results on the continuous single-valued function spaces to the continuous multifunction spaces.%利用k序列给出连续集值映射空间Ck(X)是Fréchet空间当且仅当X的每一个开k覆盖(￡)含有k序列.证明Cwk(X)是严格Fréchet空间,Ck(X)是Fréchet空间,严格Fréchet空间,强Fréchet空间当且仅当对于X的每一个开k覆盖列{(￡)n}n∈N,都存在Un∈(￡)n使得{Un}n∈N是X的k序列.将关于连续单值映射空间的某些结果推广到点紧连续集值映射空间.