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 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.