在新的紧性条件下刻划集值映射的C-半连续性

The Description of C-Semi-Continuity of Set-Valued Mappings under the Condition of New Compactness

利用已有的集值映射的C-上半连续与C-下半连续的概念,推广了文献[3]中的某些结论.本文还引进了集台一种弱的紧性概念:C-上紧、C-下紧的性质,并在F(x0)分别是C-上紧、C-下紧的较弱条件下,给出了集值映射的C-上半连续与C-下半连续的一个刻划.

In this paper, some concepts of C-upper-compactness and C-lower-compactness of set-valued mappings are used to generalize some conclusions in reference [3]. The paper also introduces into a sort of weaker concept of compactness, namely, C-upper compactness and C-lower compactness. We give the characterization of the C--pper semi-continuity and C-lower semi-continuity about set-valued mapping when F（x0） is C-upper-compact and C-lower-compact respectively.