On Topology of Fuzzy Strong b-Metric Spaces

Year 2018, Issue: 21, 59 - 67, 27.02.2018

Tarkan Oner

https://izlik.org/JA89JB46AC

Abstract

In this study, we introduce and investigate the concept of fuzzy strong b-metric space such that is a fuzzy analogy of strong b-metric spaces. By using the open balls, we define a topology on these spaces which is Hausdor® and first countable. Later we show that open balls are open and closed balls are closed. After defining the standard fuzzy strong b-metric space induced by a strong b-metric, we show that these spaces have same topology. We also note that every separable fuzzy strong b-metric space is second countable. Moreover, we give the uniform convergence theorem for these spaces.

Keywords

Fuzzy strong b-metric space , strong b-metric space , b-metric spaces , uniform convergence

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