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ON THE COMPLETION OF
$b$-METRIC SPACES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 98 / Issue 2 / October 2018
- Published online by Cambridge University Press:
- 05 July 2018, pp. 298-304
- Print publication:
- October 2018
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- Article
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- You have access
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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.
