\(I\)-\textbf{FTOP} is isomorphic to \(I\)-\textbf{FQN} and \(I\)-\textbf{AITOP}
type: Item
instance of: scholarly article
title: \(I\)-\textbf{FTOP} is isomorphic to \(I\)-\textbf{FQN} and \(I\)-\textbf{AITOP}
zbMATH Open document ID: 1079.54006
author: Jin-Ming Fang
published in: Fuzzy Sets and Systems
publication date: 2004-11-23T00:00:00Z
review text: The author gives two characterizations of \(I\)-FTOP, the cateogry of \(I\)-fuzzy topological spaces and \(I\)-fuzzy continuous mappings. Following the idea of quasi-coincident neighborhood systems introduced by the reviewer [J. Math. Anal. Appl. 76, 571--599 (1980; Zbl 0447.54006)], the author constructs the category of \(I\)-fuzzy quasi-coincident neighborhood spaces and their continuous mappings, denoted by \(I\)-FQN. Though the intuitions underlying \(I\)-FQN and \(I\)-FTOP are quite different, however, the author shows that \(I\)-FTOP is isomorphic to \(I\)-FQN. Second, the author constructs the category of antichain \(I\)-topological spaces and their continuous mappings, denoted \(I\)-AITOP, and shows that \(I\)-FTOP is isomorphic to \(I\)-AITOP.
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 2118383
zbMATH Keywords: fuzzy topology
zbMATH Keywords: quasi-neighborhood systems
zbMATH Keywords: isomorphism on category
reviewed by: Yingming Liu
MaRDI profile type: Publication
full work available at URL: j.fss.2003.09.004
OpenAlex ID: W2024556527
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DOI: 10.1016/J.FSS.2003.09.004
description: scientific article; zbMATH DE number 2118383