Endpoints in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math>-quasi-metric spaces

Agyingi, Collins Amburo; Haihambo, Paulus; Künzi, Hans-Peter A.

doi:10.1016/j.topol.2014.02.010

Cited by 12 publications

(14 citation statements)

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“…Improving on a result from [6] in this note we will show that for any join compact 0 -quasimetric space ( , ) the set of the endpoints (resp., startpoints) of is equal to the set of the endpoints (resp., startpoints) of its -hyperconvex hull ( , ).…”

Section: Introductionmentioning

confidence: 82%

“…We also specialize some of our earlier results in [6] to twovalued 0 -quasimetric spaces. It is well known that they are, essentially, the partially ordered sets and that in the category of partially ordered sets the injective hull coincides with the Dedekind-MacNeille completion (see, e.g., [5,7,8]).…”

Section: Introductionmentioning

confidence: 97%

“…In [6] the authors defined the concept of an endpoint in an arbitrary 0 -quasimetric space. In the quasimetric context it turned out to be natural to consider also the dual concept of an endpoint, which we called a startpoint.…”

Section: Introductionmentioning

confidence: 99%

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Endpoints inT0-Quasimetric Spaces: Part II

Agyingi

Haihambo

Künzi

2013

Abstract and Applied Analysis

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We continue our work on endpoints and startpoints inT0-quasimetric spaces. In particular we specialize some of our earlier results to the case of two-valuedT0-quasimetrics, that is, essentially, to partial orders. For instance, we observe that in a complete lattice the startpoints (resp., endpoints) in our sense are exactly the completely join-irreducible (resp., completely meet-irreducible) elements. We also discuss for a partially ordered set the connection between its Dedekind-MacNeille completion and theq-hyperconvex hull of its naturalT0-quasimetric space.

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Section: Introductionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 97%

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Endpoints inT0-Quasimetric Spaces: Part II

Agyingi

Haihambo

Künzi

2013

Abstract and Applied Analysis

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“…In this section, we recall some results from the theory of the q-hyperconvex hull of a T 0 -quasi-metric space due to Kemajou et al (see [3,4,8]). These are employed later to establish other results in Section 4.…”

Section: The Q-hyperconvex Hull Of An Asymmetric Spacementioning

confidence: 99%

Versatile asymmetrical tight extensions

Otafudu

Mushaandja

2017

Topological Algebra and Its Applications

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“…In addition, a recent preprint by Agyingi et al [1] investigated the tight extensions of T 0 -quasi-metric spaces. Herrmann and Moulton [4] found that tight-spans could be defined for more general maps such as directed metrics and distances.…”

Section: Preliminariesmentioning

confidence: 99%

Quasi-metric tree inT0-quasi-metric spaces

Otafudu

2013

Topology and its Applications

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MSC: 54E15 54E35 54C15 54E55 54E50 Keywords:Metric interval Metric tree T 0 -quasi-metric Quasi-metric interval Quasi-metric treeIn his well-known paper dealing with metric trees and tight extension of metric spaces, Dress studied the relationship between metric trees and hyperconvex metric spaces. In the present work, we introduce similarly the notion of quasi-metric tree of a T 0 -quasi-metric space. In particular, we show that large parts of the theory of metric trees do not use the symmetry of the metric and, under appropriate modifications, it still holds essentially unchanged for T 0 -quasi-metrics.

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Endpoints inT0-quasi-metric spaces

Cited by 12 publications

References 10 publications

Endpoints inT0-Quasimetric Spaces: Part II

Endpoints inT0-Quasimetric Spaces: Part II

Versatile asymmetrical tight extensions

Quasi-metric tree inT0-quasi-metric spaces

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