Lowen spaces
type: Item
instance of: scholarly article
title: Lowen spaces
zbMATH Open document ID: 0949.54008
author: Dexue Zhang
author: Yingming Liu
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-12-03T00:00:00Z
review text: An \(L\)-topological space \((L^X,\delta)\), where \(L\) is a completely distributive complete lattice, is said to be a Lowen space (this notion coincides with Lowen's notion of fuzzy neighborhood space [\textit{R. Lowen}, Fuzzy Sets Syst. 7, No. 2, 165-189 (1982; Zbl 0487.54008)] when \(L=[0,1]\)) if \(\delta\) has a base \(\beta\subset\{_aU \mid a\in L\), \(U\subset X\}\). The authors prove several characterizations of Lowen spaces, and thus show that the category of Lowen spaces is isomorphic to the category of \(L\)-fuzzifying topological spaces.
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 1423866
zbMATH Keywords: fuzzy neighborhood space
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6586
OpenAlex ID: W3022499565
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DOI: 10.1006/JMAA.1999.6586
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description: scientific article; zbMATH DE number 1423866