The stratified canonical fuzzy topology on \(I(I)\) is uniformizable
type: Item
instance of: scholarly article
title: The stratified canonical fuzzy topology on \(I(I)\) is uniformizable
zbMATH Open document ID: 0766.54007
DOI: 10.1016/0022-247X(92)90006-Y
author: Dexue Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-04-01T00:00:00Z
review text: Let \(L\) be a completely distributive lattice with an order reversing involution, \(I(L)\) an \(L\)-fuzzy unit interval. \textit{S. E. Rodabaugh} posed a question whether or not the stratified canonical fuzzy topology on \(I(L)\) is uniformizable [see J. Math. Anal. Appl. 129, 37-70 (1988; Zbl 0637.54007)]. The author gives a positive answer for the case \(L=I\). Moreover, he has also proved the uniformity obtained has a countable base, therefore, the corresponding topology on \(I(I)\) is metrizable. The author claims that his proof depends on the property of the real \(I\) and the argument holds only for the case \(L=I\). But, the recent work of the author [Fuzzy Sets Syst. 54, 225-227 (1993)] shows that for general case, there is still a positive answer to Rodabaugh's question.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54E15
zbMATH DE Number: 150640
zbMATH Keywords: fuzzy uniformity
zbMATH Keywords: \(L\)-fuzzy unit interval
zbMATH Keywords: stratified canonical fuzzy topology
reviewed by: Yingming Liu
MaRDI profile type: Publication
cites work: Metric spaces in fuzzy set theory
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cites work: Q5186352
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cites work: A theory of fuzzy uniformities with applications to the fuzzy real lines
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full work available at URL: 0022-247x(92)90006-y
OpenAlex ID: W2016178301
description: scientific article; zbMATH DE number 150640