A contribution to the study of fuzzy metric spaces (Q2756146)

By modifying the concept of metric fuzziness introduced by \textit{I. Kramosil} and \textit{J. Michalek} [Kybernetika, Praha 11, 336-344 (1975; Zbl 0319.54002)] a notion of fuzzy metric space [\textit{A. George} and the reviewer, Fuzzy Sets Syst. 64, No. 3, 395-399 (1994; Zbl 0843.54014)] has been introduced. \textit{V. Gregori} and \textit{S. Romaguera} have studied [ibid. 115, No. 3, 485-489 (2000; Zbl 0985.54007), see below] some properties of this type of fuzzy metric spaces and their work has created considerable interest in the study of fuzzy metric spaces. In this paper the author gives some interesting examples of fuzzy metric spaces and studies some questions related to boundedness and Cauchy sequences in fuzzy metric spaces. The author also introduces a concept -- non-Archimedean fuzzy metric space -- and proves that the family of these spaces agrees with the class of non-Archimedean metric spaces.