The closed finite-to-one mappings and their applications

作     者：YANG Jie LIN Shou 

作者机构：School of Mathematics and StatisticsMinnan Normal UniversityZhangzhouFujian 363000China Department of MathematicsNingde Normal UniversityNingdeFujian 352100China 

出 版 物：《Applied Mathematics(A Journal of Chinese Universities)》 (高校应用数学学报（英文版）（B辑）)

年 卷 期：2019年第34卷第2期

页      面：149-161页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(11801254 11471153) 

主　　题：finite-to-one mappings closed mappings weak first-countability sn-networks cs-networks symmetric products 

摘      要：In this paper, we discuss the closed finite-to-one mapping theorems on generalized metric spaces and their applications. It is proved that point-Gδ properties,?0-snf-countability and csf-countability are invariants and inverse invariants under closed finite-to-one mappings. By the relationships between the weak first-countabilities, we obtain the closed finite-to-one mapping theorems of weak quasi-first-countability, quasi-first-countability, snf-countability, gfcountability and sof-countability. Furthermore, these results are applied to the study of symmetric products of topological spaces.