On the completion of fuzzy metric spaces
type: Item
instance of: scholarly article
title: On the completion of fuzzy metric spaces
zbMATH Open document ID: 1177.54002
author: Huan Huang
author: Congxin Wu
published in: Fuzzy Sets and Systems
publication date: 2009-08-28T00:00:00Z
review text: The main result is the following: Suppose that \((x,d,L,R)\) is a fuzzy metric space. Suppose that \(\{\lambda_0(x_n,y_n) \}^\infty_{n=1}\) and \(\{\rho_0(x_n,y_n)\}^\infty_{n=1}\) are left equicontinuous, whenever \(\{x_n\}\) and \(\{y_n\}\) are Cauchy sequences. Then \((x,d,L,R)\) has a completion which is uniquely determined up to isometry. Also \((x,d,L,R)\) has a unique completion if and only if \(\{\rho_0(x_n,y_n)\}\) is left equicontinuous on \((0,1]\).
reviewed by: K. Chandrasekhara Rao
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54E50
zbMATH DE Number: 5599478
zbMATH Keywords: fuzzy metric spaces
zbMATH Keywords: fuzzy numbers
zbMATH Keywords: completion
zbMATH Keywords: isometry
zbMATH Keywords: Cauchy sequence
MaRDI profile type: Publication
full work available at URL: j.fss.2008.05.008
OpenAlex ID: W2066797282
cites work: Q4870855
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DOI: 10.1016/J.FSS.2008.05.008
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description: scientific article; zbMATH DE number 5599478