The prime dicompletion of a di-uniformity on a plain texture
type: Item
instance of: scholarly article
title: The prime dicompletion of a di-uniformity on a plain texture
zbMATH Open document ID: 1225.54006
author: Selma Özçağ
author: Lawrence M. Brown
published in: Topology and its Applications
publication date: 2011-08-04T00:00:00Z
review text: This paper deals with the problem of constructing a dicompletion for a di-uniformity \(\upsilon\) on a texture \((S,\mathcal{S})\). The problem appears to be hard and the authors confine their attention to plain textures (the ones for which the texturing is closed under arbitrary unions). They construct a completion of \(\upsilon\) in terms of prime \(\mathcal S\)-filters. When \(\upsilon\) is separated, a separated completion is obtained using the \(T_0\)-quotient, and it is proved that this construction produces a reflector making the category of separated complete di-uniform spaces a full reflective subcategory of the category of separated di-uniform spaces. Then it is noted, as expected, that for totally bounded di-uniformities these constructions lead to dicompactifications of the uniform ditopology.
reviewed by: Jorge Picado
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 06D10
Mathematics Subject Classification ID: 03E20
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 5935903
zbMATH Keywords: plain texture
zbMATH Keywords: di-uniformity
zbMATH Keywords: maximal regular difilter
zbMATH Keywords: prime dicompletion
zbMATH Keywords: prime filter
MaRDI profile type: Publication
full work available at URL: j.topol.2011.05.028
OpenAlex ID: W2077521961
cites work: Q4693062
cites work: Q3595081
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DOI: 10.1016/J.TOPOL.2011.05.028
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description: scientific article; zbMATH DE number 5935903