\(L\)-proximities and totally bounded pointwise \(L\)-uniformities
type: Item
instance of: scholarly article
title: \(L\)-proximities and totally bounded pointwise \(L\)-uniformities
zbMATH Open document ID: 1041.54013
DOI: 10.1016/S0165-0114(02)00282-8
author: Fu-Gui Shi
author: Jie Zhang
author: Chong You Zheng
published in: Fuzzy Sets and Systems
publication date: 2003-02-13T00:00:00Z
review text: The connections between \(L\)-(quasi-)proximities in the sense of Katsaras-Liu-Artico-Moresco and pointwise \(L\)-(quasi-)uniformities in the sense of Shi are investigated. A pointwise (quasi-) uniform space \((L^x,{\mathcal U})\) and an \(L\)-(quasi-)proximity space \((L^x,\delta)\) are considered. For an \(L\)-proximity \(\delta\) on \(L^x\), a pointwise \(L\)-quasi-uniformity \({\mathcal U}_\delta\) is defined. It is proved that \(\delta\) and \({\mathcal U}_\delta\) induce the same topology. An \(L\)-topology can be induced by an \(L\)-proximity iff it is pointwise completely regular. For any \(L\)-(quasi-)proximity \(\delta\), the \(L\)-(quasi-)uniformity \({\mathcal U}_\delta\) is totally bounded.
reviewed by: Dušan Adnadjević
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 1868238
zbMATH Keywords: \(L\)-topology
zbMATH Keywords: pointwise \(L\)-(quasi-)uniformity
zbMATH Keywords: \(L\)-(quasi-)proximity
MaRDI profile type: Publication
Wikidata QID: Q57587827
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DBLP publication ID: journals/fss/ShiZZ03
description: scientific article; zbMATH DE number 1868238