利用单位分解定理得到从紧的Hausdorff拓扑空间到没有任何凸结构的有限连续拓扑空间(简称,FC-空间)的集值映射的连续选择定理,并从该结果和Tychonoff不动点定理,得到紧的FC-空间的乘积空间上映射族的集族不动点定理和若干个非紧的FC-空间的乘积空间上的映射族的集族不动点定理,对文献中的相应结果进行了改进和一般化.
By using the partition theorem of unity, a continuous selection theorem for a muhimap from a compact Hausdorff topological space to a finitely continuous topological spaces ( simply, FC- spaces) without any convexity structure was obtained, and from which and Tychonoff fixed point theorem, a collectively fixed point theorem for a family of multimaps on the product space of compact FC-spaees and several collectively fixed point theorems for a family of multimaps on the product space of non-compact FC-spaces were given. These results generalize and improve the corresponding conclusions in the recent literature.