Some new results on $\star$-metric spaces

Year 2023, Volume: 12 Issue: 3, 157 - 165, 31.12.2023

Abhishikta Das , Tarapada Bag

https://doi.org/10.54187/jnrs.1367114

Abstract

The concept of $\star$-metric, based on the relaxation of triangle inequality of metric axioms by using a t-definer, was introduced by Khatami and Mirzavaziri. This paper extends and generalizes some well-known results of classical metric space. Considering the definition of $\star$-metric space, it studies the notion of a closed ball. The paper proves some results related to closed sets, convergent sequences, Cauchy sequences, and the diameter of a set. This paper contains the study on the metrizability of $\star$-metric space and provides an alternative approach to the proof of metrizability for $\star$-metric space using the famous `Niemytski and Wilson's metrization theorem'.

Keywords

t-definer, $\star$-metric space, closed set, metrizability

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