The main purpose of this article is to provide alternative proofs of the metrizability of metric-like spaces like -metric spaces,
-metric spaces, and
-metric spaces. We improve upon the metrizability result of An et al. [Topology Appl. 185–186 (2015)] for
-metric spaces. Moreover, we provide two shorter proofs of the metrizability of
-metric spaces, recently introduced by Jleli and Samet. Furthermore, we give a partial answer to an open problem regarding the openness of
-open balls in
-metric spaces. Finally, we give an alternative proof of the metrizability of
-metric spaces.
Some remarks on the metrizability of some metric-like structures
Som, Sumit, Petruşel, Adrian and Dey, Lakshmi Kanta
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Author(s) | Dey, Lakshmi Kanta, Petruşel, Adrian, Som, Sumit |
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DOI | https://doi.org/10.37193/CJM.2021.02.12 |