Endpoints in \(T_0\)-quasimetric spaces. II.
type: Item
instance of: scholarly article
title: Endpoints in \(T_0\)-quasimetric spaces. II.
zbMATH Open document ID: 1300.54035
DOI: 10.1155/2013/539573
author: Collins Amburo Agyingi
author: Paulus Haihambo
author: Hans Peter Künzi
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: The authors continue their study of endpoints and the q-hyperconvex hull of a \(T_0\)-quasimetric space, initiated in [\textit{C. A. Agyingi} et al., Topology Appl. 168, 82--93 (2014; Zbl 1292.54016)]. In this paper, they study the concept of collinearity in quasi-pseudometric spaces and show that for a join compact \(T_0\)-quasimetric space, the points in the remainder of its q-hyperconvex hull lie between a startpoint and an endpoint of the space. They also prove that the q-hyperconvex hull of a join compact \(T_0\)-quasi-metric space has the same endpoints and startpoints as the space. Then they study startpoints and endpoints in the natural \(T_0\)-quasimetric of a partially ordered set, giving a characterization in terms of the partial order and providing various examples for different partially ordered sets. Finally, the authors study the relation between the MacNeille completion of a partially ordered set and the q-hyperconvex hull of its natural \(T_0\)-quasimetric.
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54E50
zbMATH DE Number: 6306986
zbMATH Keywords: quasi-metric
zbMATH Keywords: endpoint
zbMATH Keywords: start point
zbMATH Keywords: partially ordered set
zbMATH Keywords: hyperconvex hull
reviewed by: Miguel Angel Sanchez Granero
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/539573
OpenAlex ID: W1514850728
Wikidata QID: Q58917076
cites work: Six theorems about injective metric spaces
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: Hyperconvex hulls of metric spaces
cites work: The Isbell-hull of a di-space
cites work: Tight spans, Isbell completions and semi-tropical modules
cites work: Endpoints in \(T_0\)-quasi-metric spaces
cites work: Q3730636
cites work: Approaching metric domains
cites work: Q4530231
cites work: Q3966761
cites work: Q5191281
cites work: Functional Analysis in Asymmetric Normed Spaces
cites work: Introduction to hyperconvex spaces
cites work: An Introduction to Metric Spaces and Fixed Point Theory
cites work: Extension of uniformly continuous transformations and hyperconvex metric spaces
cites work: On externally complete subsets and common fixed points in partially ordered sets
cites work: On tight spans for directed distances
cites work: \(q\)-hyperconvexity in quasipseudometric spaces and fixed point theorems
cites work: Addendum to ‘The Katětov construction modified for a T0-quasi-metric space’
cites work: Q4982342
cites work: The Katětov construction modified for a \(T_0\)-quasi-metric space
cites work: Quantitative Concept Analysis
cites work: The ultra-quasi-metrically injective hull of a \(T_0\)-ultra-quasi-metric space
cites work: Continuous Lattices and Domains
Recommended article: Endpoints in \(T_0\)-quasi-metric spaces
Recommended article: Extensions of \(T_0\)-quasi-metrics
Recommended article: Q4982342
Recommended article: Q5152137
Recommended article: Quasi-metric spaces and point-free geometry
Recommended article: End point results in metric spaces endowed with a graph
Recommended article: Some fixed point results in \(D^*\)-quasimetric spaces
Recommended article: Convexity structures in \(T_{0}\)-quasi-metric spaces
Recommended article: Q3175545
Recommended article: On di-injective \(T_{0}\)-quasi-metric spaces
description: scientific article; zbMATH DE number 6306986