Back to Search
Start Over
so-metrizable spaces and images of metric spaces
- Source :
- Open Mathematics, Vol 19, Iss 1, Pp 1145-1152 (2021)
- Publication Year :
- 2021
- Publisher :
- De Gruyter, 2021.
-
Abstract
- so-metrizable spaces are a class of important generalized metric spaces between metric spaces and snsn-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 XX 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 snsn-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, snsn-open mapping and 2-sequence-covering mapping, which further enrich and deepen generalized metric space theory.
Details
- Language :
- English
- ISSN :
- 23915455
- Volume :
- 19
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Open Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.281749b77a9d47d2b6e882858500d31b
- Document Type :
- article
- Full Text :
- https://doi.org/10.1515/math-2021-0082