Abstract
The notion of uniform continuity in fuzzy metric spaces was first introduced by George and Veeramani in 1995. Later, Gregori et al. gave some contributions to the theory. As a consequence of the study, we introduce the notion of RUC fuzzy metric space. Also, necessary and sufficient conditions for a fuzzy metric space to be an RUC fuzzy metric space are studied. In addition, several examples are given.
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