On Topology of Fuzzy Strong b-Metric Spaces

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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