On the goodness of some types of fuzzy paracompactness
type: Item
instance of: scholarly article
title: On the goodness of some types of fuzzy paracompactness
zbMATH Open document ID: 0809.54007
DOI: 10.1016/0165-0114(93)90131-Z
author: M. W. Warner
author: Ali Bülbül
published in: Fuzzy Sets and Systems
publication date: 1994-01-27T00:00:00Z
review text: The authors introduce the definitions of paracompactness, almost paracompactness, nearly paracompactness, semi-paracompactness, para-\(S\)- closedness, weakly paracompactness and \(RS\)-paracompactness in fuzzy setting along the lines of Lowen's fuzzy compactness. To introduce the above concepts the authors adopt the concept of locally finite families of fuzzy sets and the concept of refinement introduced by Malghan and Benchalli. For a topological space \((X,\tau)\) and its generated fuzzy topological space \(\omega (t)\) the authors prove that ``\((X,\omega(t))\) is paracompact if and only if \((X,\tau)\) is paracompact. Thus fuzzy paracompactness is a good extension of paracompactness''. The authors produce analogous forms of good extensions of the other concepts introduced in this work. They conjecture that fuzzy \(RS\)-paracompactness is also good, they could'nt complete a proof of this.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54D20
zbMATH DE Number: 487525
zbMATH Keywords: fuzzy paracompactness
zbMATH Keywords: good extension
zbMATH Keywords: \(RS\)-paracompactness
reviewed by: S. Saha
MaRDI profile type: Publication
cites work: Some good dilutions of fuzzy compactness
cites work: A comparison of different compactness notions in fuzzy topological spaces
cites work: Q3962151
cites work: Q5605131
full work available at URL: 0165-0114(93)90131-z
OpenAlex ID: W2086199353
description: scientific article; zbMATH DE number 487525