The main purpose of this article is to provide alternative proofs of the metrizability of metric-like spaces like b-metric spaces, \mathcal{F}-metric spaces, and \theta-metric spaces. We improve upon the metrizability result of An et al. [Topology Appl. 185–186 (2015)] for b-metric spaces. Moreover, we provide two shorter proofs of the metrizability of \mathcal{F}-metric spaces, recently introduced by Jleli and Samet. Furthermore, we give a partial answer to an open problem regarding the openness of \mathcal{F}-open balls in \mathcal{F}-metric spaces. Finally, we give an alternative proof of the metrizability of \theta-metric spaces.

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  Dey, Lakshmi Kanta,  Petruşel, Adrian,  Som, Sumit