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-G 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, gf-
countability and sof-countability. Furthermore, these results are applied to the study of symmetric
products of topological spaces.
关键词：
finite-to-one mappings,
closed mappings,
weak rst-countability,
sn-networks,
cs-networks,
symmetric products
