On $b_2$-Metric Spaces

Year 2021, Volume: 9 Issue: 1, 33 - 39, 28.04.2021

Elif Güner , Halis Aygün

Abstract

The target of this paper is to induce a topology from a given $b_2$-metric and study the properties of the topology induced by this way. We first define the notion of $\varepsilon$-ball in $b_2$-metric spaces and consider the topology induced by a given $b_2$-metric via $\varepsilon$-balls. We study some properties of this topological space such as separation axioms and semi-metrizability. Also, we show with the examples that some known properties for $\varepsilon$-balls in metric spaces have not existed in $b_2$-metric spaces. Then we introduce the concept of strong $b_2$-metric spaces in which these known properties are provided. Finally, we show that every strong $b_2$-metric topological space is normal, metrizable and of second category.

Keywords

b_2-metric spaces, strong b_2-metric spaces, Hausdorff Spaces, Metrizable topological spaces

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