Some new results on $\\star$-metric spaces

Authors : Abhishikta Das, Tarapada Bag

Pages : 157-165

Doi:10.54187/jnrs.1367114

View : 60 | Download : 62

Publication Date : 2023-12-31

Article Type : Research

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