so-metrizable spaces and images of metric spaces
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 int...
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| Autores principales: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/281749b77a9d47d2b6e882858500d31b |
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| Sumario: | 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. |
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