Ultra-quasi-metrically tight extensions of ultra-quasi-metric spaces
type: Item
instance of: scholarly article
title: Ultra-quasi-metrically tight extensions of ultra-quasi-metric spaces
zbMATH Open document ID: 1356.54032
DOI: 10.1155/2015/646018
author: Collins Amburo Agyingi
published in: Chinese Journal of Mathematics
publication date: 2016-04-14T00:00:00Z
reviewed by: Othman Echi
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54E50
Mathematics Subject Classification ID: 54C15
Mathematics Subject Classification ID: 54E55
zbMATH DE Number: 6568846
zbMATH Keywords: injective hull
zbMATH Keywords: tight extension
zbMATH Keywords: ultra-quasi-pseudometric
Wikidata QID: Q59104994
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/646018
OpenAlex ID: W1942163404
cites work: Q4982342
cites work: Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces
cites work: Approximating dissimilarities by quasi-ultrametrics
cites work: The ultra-quasi-metrically injective hull of a \(T_0\)-ultra-quasi-metric space
cites work: Generalized metric spaces: Completion, topology, and powerdomains via the Yoneda embedding
review text: In [Adv. Math. 53, 321--402 (1984; Zbl 0562.54041)], \textit{A. W. M. Dress} has introduced the concept of tight extension of a metric space which is equivalent to a concept introduced by \textit{J. R. Isbell} [Comment. Math. Helv. 39, 65--76 (1964; Zbl 0151.30205)], namely the injective hull of a metric space. In 2014, the author together with \textit{P. Haihambo} and \textit{H.-P. A. Künzi} [in: V. Brattko (ed.) et al., Logic, computation, hierarchies. Dedicated to Victor L. Selivanov on the occasion of his 60th birthday. Berlin: De Gruyter. Ontos Mathematical Logic 4, 9--22 (2014; Zbl 1320.54018)] has constructed the tight extensions of quasi-metric spaces. In the present paper, the author does an appropriate modification, in order to come up with a tight extension for \(\mathbf{UQP}\)-metric spaces (\(T_0\)-ultra-quasi-metric spaces). Using techniques similar to those of Dress, the author shows that every \(\mathbf{UQP}\)-metric space \(X\) has a \(uq\)-tight extension which is maximal in the class of \(uq\)-tight extensions of \(X\).NEWLINENEWLINERemark that similar constructions in the category of \(T_0\)-ultra-quasi-metric spaces and contracting maps have been done by \textit{H.-P. A. Künzi} and \textit{O. O. Otafudu} [Appl. Categ. Struct. 21, No. 6, 651--670 (2013; Zbl 1284.54040)]. In this paper the author does the constructions in the category of \(\mathbf{UQP}\)-metric spaces and nonexpansive maps
description: scientific article; zbMATH DE number 6568846