Cover quasi-uniformities in frames
type: Item
instance of: scholarly article
title: Cover quasi-uniformities in frames
zbMATH Open document ID: 1215.06005
author: Jorge Picado
author: A. Pultr
published in: Topology and its Applications
publication date: 2011-05-16T00:00:00Z
review text: Quasi-uniformities (that is, not necessarily symmetric uniformities) on a set \(X\) are normally studied via entourages (that is, special subsets of \(X\times X\)). This has been done successfully in the point-free context, too. However, because the point-free representation of the square \(X\times X\) is not without difficulties, there was an interest in an approach to quasi-uniformities via covers. Based on the (spatial) ideas from Ganter and Steinlage, a cover-type quasi-uniformity was developed by Frith (and others) using biframes, the point-free variant of bitopologies. In the present paper, the authors show that this detour can be avoided by giving a variant of the paircover definition that avoids the need of a biframe structure. Indeed they present a concept of a cover-type quasi-uniformity structure that is directly defined in frames. Their new approach is then shown to be equivalent to the one based on the notion of a biframe.
Mathematics Subject Classification ID: 06D22
Mathematics Subject Classification ID: 54E05
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54E55
zbMATH DE Number: 5888192
zbMATH Keywords: entourage
zbMATH Keywords: biframe
zbMATH Keywords: quasi-uniformities
zbMATH Keywords: covers
zbMATH Keywords: paircover
reviewed by: Hans Peter Künzi
MaRDI profile type: Publication
full work available at URL: j.topol.2011.01.007
OpenAlex ID: W2081256797
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DOI: 10.1016/J.TOPOL.2011.01.007
description: scientific article; zbMATH DE number 5888192