Stone-type theorem on b-metric spaces and applications

In this paper, we first show that every b-metric space with the topology induced by its convergence is a semi-metrizable space and thus many properties of b-metric spaces used in the literature are obvious. Then, we prove the Stone-type theorem on b-metric spaces and get a sufficient condition for a...

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Bibliographic Details
Published inTopology and its applications Vol. 185-186; pp. 50 - 64
Main Authors An, Tran Van, Tuyen, Luong Quoc, Dung, Nguyen Van
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.05.2015
Subjects
b-Metric space
Metric-type space
Metrization
secondary
b-Metric space
Metrization
Metric-type space
primary
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Summary:In this paper, we first show that every b-metric space with the topology induced by its convergence is a semi-metrizable space and thus many properties of b-metric spaces used in the literature are obvious. Then, we prove the Stone-type theorem on b-metric spaces and get a sufficient condition for a b-metric space to be metrizable. We also give answers to the question posed by Khamsi and Hussain in [24] and discuss some results relating to the metrization of 2-metric spaces and S-metric spaces.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2015.02.005