On initial and final fuzzy uniform structures
type: Item
instance of: scholarly article
title: On initial and final fuzzy uniform structures
zbMATH Open document ID: 1029.54011
DOI: 10.1016/S0165-0114(02)00329-9
author: Fatma Bayoumi
published in: Fuzzy Sets and Systems
publication date: 2003-02-13T00:00:00Z
review text: The paper is devoted to the study of initial and final structures in the category FUN of fuzzy uniform spaces introduced in [\textit{W. Gähle}, \textit{F. Bayoumi}, \textit{A. Kandil} and \textit{A. Nouh}, ibid. 97, 225-254 (1998; Zbl 0934.54004)]. The existence of initial and final lifts (and hence the existence of initial and final structures) in the category FUN is proved. By means of special initial structures subspaces and products in FUN are characterized. It is shown that the fuzzy topology \({\mathcal T}_{{\mathcal U}}\) generated by the fuzzy uniform structure \({\mathcal U}\), which is initial for a family of fuzzy uniform structures \(\{{\mathcal U}_i, i\in{\mathcal I}\}\), is initial for the family of corresponding generated fuzzy topologies \(\{{\mathcal T}_{{\mathcal U}_i}, i\in{\mathcal I}\}\).
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 18B30
zbMATH DE Number: 1868237
zbMATH Keywords: fuzzy uniform structure
zbMATH Keywords: global fuzzy neighborhood structure
zbMATH Keywords: initial structure
zbMATH Keywords: final structure
reviewed by: Alexander Šostak
MaRDI profile type: Publication
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full work available at URL: s0165-0114(02)00329-9
OpenAlex ID: W2094091150
description: scientific article; zbMATH DE number 1868237