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00925njm 22002777a 4500 dc Gregori, Valentin author Minana, Juan-Jose author Roig, Bernardino author Sapena, Almanzor author 2020-06 Here, we deal with the concept of fuzzy metric space(X,M,*), due to George and Veeramani. Based on the fuzzy diameter for a subset ofX, we introduce the notion of strong fuzzy diameter zero for a family of subsets. Then, we characterize nested sequences of subsets having strong fuzzy diameter zero using their fuzzy diameter. Examples of sequences of subsets which do or do not have strong fuzzy diameter zero are provided. Our main result is the following characterization: a fuzzy metric space is strongly complete if and only if every nested sequence of close subsets which has strong fuzzy diameter zero has a singleton intersection. Moreover, the standard fuzzy metric is studied as a particular case. Finally, this work points out a route of research in fuzzy fixed point theory. Gregori V, Minana JJ, Roig B, Sapena A. A Characterization of Strong Completeness in Fuzzy Metric Spaces. Mathematics. 2020 Jun;8(6):861. 10.3390/math8060861 2227-7390 Mathematics https://hdl.handle.net/20.500.13003/19400 2-s2.0-85087067491 https://hdl.handle.net/20.500.12105/22968 553515900001 Fuzzy metric Cauchy sequence (strong) convergence Completeness Fuzzy diameter A Characterization of Strong Completeness in Fuzzy Metric Spaces