Some properties of fuzzy metric spaces
type: Item
instance of: scholarly article
title: Some properties of fuzzy metric spaces
zbMATH Open document ID: 0985.54007
DOI: 10.1016/S0165-0114(98)00281-4
author: Salvador Romaguera
author: Valentín Gregori
published in: Fuzzy Sets and Systems
publication date: 2002-05-27T00:00:00Z
review text: One of the main problems in the theory of fuzzy topological spaces is to obtain an appropriate and consistent notion of fuzzy metric space. Many authors have investigated this question and several different notions of a fuzzy metric space have been defined and studied. In [\textit{A. George} and the reviewer, ibid. 64, No. 3, 395-399 (1994; Zbl 0843.54014)] 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)] an interesting notion of fuzzy metric space has been studied. In [J. Fuzzy Math. 3, No. 4, 933-940 (1995; Zbl 0870.54007)] \textit{A. George} and the reviewer, have proved that every such metric space is metrizable. In this paper the authors give a more natural proof for this result. In addition to this result the authors prove some interesting results like: every separable fuzzy metric space admits a compatible precompact fuzzy metric and, a fuzzy metric space is compact if ond only if it is precompact and totally bounded. In particular, the celebrated Niemytzki-Tychonoff theorem is generalized to the fuzzy setting.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 1545769
reviewed by: P. Veeramani
MaRDI profile type: Publication
cites work: Q4150804
cites work: On some results in fuzzy metric spaces
cites work: On some results of analysis for fuzzy metric spaces
cites work: Fixed points in fuzzy metric spaces
cites work: Q3226265
cites work: Statistical metric spaces
Wikidata QID: Q126298393
full work available at URL: s0165-0114(98)00281-4
OpenAlex ID: W2049442812
description: scientific article; zbMATH DE number 1545769