Acta Mathematica Hungarica
Volume/Issue:
Volume 127: Issue 3
The scale of a quasi-uniform space
Authors:
H. Künzi University of Cape Town Department of Mathematics and Applied Mathematics Rondebosch 7701 South Africa

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O. Otafudu University of Cape Town Department of Mathematics and Applied Mathematics Rondebosch 7701 South Africa

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Pages:
239–259
Online Publication Date:
19 Mar 2010
Publication Date:
01 May 2010
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-010-9131-9
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Abstract  

We investigate the left-sided scale and the two-sided scale of a quasi-uniform space. While the two-sided scale of a quasi-uniform space X shows a behavior similar to the usual hyperspace of X equipped with its Hausdorff quasiuniformity, the left-sided scale generalizes the quasi-uniform multifunction space of X into itself. Either construction of the scale relies on the concept of the prefilter space of a quasi-uniform space. Prefilter spaces of quasi-uniform spaces are proved to be bicomplete. Consequently both the left-sided and the two-sided scale of a quasiuniform space are bicomplete. Indeed these scales can be used to construct the bicompletion of the T0-refiection of the Hausdorff quasi-uniformity of a quasiuniform space.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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