Abstract
so-metrizable spaces are a class of important generalized metric spaces between metric spaces and
s
n
sn
-metrizable spaces where a space is called an so-metrizable space if it has a
σ
\sigma
-locally finite so-network. As the further work that attaches to the celebrated Alexandrov conjecture, it is interesting to characterize so-metrizable spaces by images of metric spaces. This paper gives such characterizations for so-metrizable spaces. More precisely, this paper introduces so-open mappings and uses the “Pomomarev’s method” to prove that a space
X
X
is an so-metrizable space if and only if it is an so-open, compact-covering,
σ
\sigma
-image of a metric space, if and only if it is an so-open,
σ
\sigma
-image of a metric space. In addition, it is shown that so-open mapping is a simplified form of
s
n
sn
-open mapping (resp. 2-sequence-covering mapping if the domain is metrizable). Results of this paper give some new characterizations of so-metrizable spaces and establish some equivalent relations among so-open mapping,
s
n
sn
-open mapping and 2-sequence-covering mapping, which further enrich and deepen generalized metric space theory.