On the Completion of -Metric Spaces

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.