The closed finite-to-one mappings and their applications
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, ℵ0-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, gf-countability and sof-countability. Furthermore, these results are applied to the study of symmetric products of topological spaces.
Keywordsfinite-to-one mappings closed mappings weak first-countability sn-networks cs-networks symmetric products
MR Subject Classification54B05 54B10 54C10 54D55 54D99 54E99 54G20
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The authors would like to thank the referees for some constructive suggestions and all their efforts in order to improve this paper.
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