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:	Yang Songlin, Ge Xun
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	so-network so-metrizable space so-open mapping compact-covering mapping σ-mapping 54e35 54e40 54e45 54e50 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/281749b77a9d47d2b6e882858500d31b
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spelling	oai:doaj.org-article:281749b77a9d47d2b6e882858500d31b2021-12-05T14:10:53Zso-metrizable spaces and images of metric spaces2391-545510.1515/math-2021-0082https://doaj.org/article/281749b77a9d47d2b6e882858500d31b2021-11-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0082https://doaj.org/toc/2391-5455so-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.Yang SonglinGe XunDe Gruyterarticleso-networkso-metrizable spaceso-open mappingcompact-covering mappingσ-mapping54e3554e4054e4554e50MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 1145-1152 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	so-network so-metrizable space so-open mapping compact-covering mapping σ-mapping 54e35 54e40 54e45 54e50 Mathematics QA1-939
spellingShingle	so-network so-metrizable space so-open mapping compact-covering mapping σ-mapping 54e35 54e40 54e45 54e50 Mathematics QA1-939 Yang Songlin Ge Xun so-metrizable spaces and images of metric spaces
description	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.
format	article
author	Yang Songlin Ge Xun
author_facet	Yang Songlin Ge Xun
author_sort	Yang Songlin
title	so-metrizable spaces and images of metric spaces
title_short	so-metrizable spaces and images of metric spaces
title_full	so-metrizable spaces and images of metric spaces
title_fullStr	so-metrizable spaces and images of metric spaces
title_full_unstemmed	so-metrizable spaces and images of metric spaces
title_sort	so-metrizable spaces and images of metric spaces
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/281749b77a9d47d2b6e882858500d31b
work_keys_str_mv	AT yangsonglin sometrizablespacesandimagesofmetricspaces AT gexun sometrizablespacesandimagesofmetricspaces
_version_	1718371591584219136

so-metrizable spaces and images of metric spaces

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