2026-05-17T05:52:39Zhttps://repisalud.isciii.es/rest/oai/requestoai:repisalud.isciii.es:20.500.12105/229682024-11-29T04:32:57Zcom_20.500.12105_15322com_20.500.12105_2051col_20.500.12105_16967
Repisalud
author
Gregori, Valentin
author
Minana, Juan-Jose
author
Roig, Bernardino
author
Sapena, Almanzor
2024-09-13T09:14:43Z
2024-09-13T09:14:43Z
2020-06
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
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.
eng
Fuzzy metric
Cauchy sequence
(strong) convergence
Completeness
Fuzzy diameter
A Characterization of Strong Completeness in Fuzzy Metric Spaces
research article