On $b_2$-Metric Spaces

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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Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

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