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ON THE COMPLETION OF $b$-METRIC SPACES
Published online by Cambridge University Press: 05 July 2018
Abstract
Based on the metrisation of $b$-metric spaces of Paluszyński and Stempak [‘On quasi-metric and metric spaces’, Proc. Amer. Math. Soc.137(12) (2009), 4307–4312], we prove that every $b$-metric space has a completion. Our approach resolves the limitation in using the quotient space of equivalence classes of Cauchy sequences to obtain a completion of a $b$-metric space.
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- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 98 , Issue 2 , October 2018 , pp. 298 - 304
- Copyright
- © 2018 Australian Mathematical Publishing Association Inc.
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