连续选择和聚合不动点定理

Continuous Selection and Collectively Fixed Point Theorems

得到了定义域为非紧、非仿紧,值域为拓扑空间的集值映象的连续选择定理,并且集值映象的连续选择映象的定义域为整个空间而非拓扑空间的一个紧子集.应用连续选择定理,得到了聚合不动点定理,推广了最近一些文献上的相关结论.

In this paper, we obtain continuous sectection theorems for the set-value mappings whose domains are non-compact or non-paracompact and the ranges are tepological spaces. Furthermore the domain of the continuous selection mapping is not the compact subset of topological space but the whole topological space. Using the continous selection theorems, some collectively fixed point theorems are obtained which are generalizations of many known results.