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-G_δ properties,■-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.
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.
基金
Supported by the National Natural Science Foundation of China(11801254,11471153)
