A New Proof for the Characterization of Linear Betweenness Structure

A New Proof for the Characterization of Linear Betweenness Structure

In their paper published in 1997, Richmond and Richmond classified metric spaces in which all triangles are degenerate. That result was later reproved by Dovgoshei and Dordovskii in the finite case and it was generalized to finite pseudometric betweennesses by Beaudou et al. In this paper, we give a...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2020-05
1. Verfasser: Szabó, Péter G N
Format: Artikel
Sprache:eng
Schlagworte:
Linearity
Metric space
Structural analysis
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Szabó, Péter G N
description In their paper published in 1997, Richmond and Richmond classified metric spaces in which all triangles are degenerate. That result was later reproved by Dovgoshei and Dordovskii in the finite case and it was generalized to finite pseudometric betweennesses by Beaudou et al. In this paper, we give a new, independent proof to the finite case of the original theorem which we reformulate in terms of linearity of betweenness structures.
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2075646359</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2075646359</sourcerecordid><originalsourceid>FETCH-proquest_journals_20756463593</originalsourceid><addsrcrecordid>eNqNyrEKwjAQgOEgCBbtOxw4F2LStDpqVRxEBN1LKFfaIoleLhR8eh18AKd_-P6JSJTWq2ydKzUTaQiDlFIVpTJGJ2K_hQuOcCXvW2g9AXcIVWfJNozUvy333sHXzr1DS7BDHhGdwxDgxhQbjoQLMW3tI2D661wsj4d7dcqe5F8RA9eDj-S-VCtZmiIvtNno_64P-fA6Tw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2075646359</pqid></control><display><type>article</type><title>A New Proof for the Characterization of Linear Betweenness Structure</title><source>Free E- Journals</source><creator>Szabó, Péter G N</creator><creatorcontrib>Szabó, Péter G N</creatorcontrib><description>In their paper published in 1997, Richmond and Richmond classified metric spaces in which all triangles are degenerate. That result was later reproved by Dovgoshei and Dordovskii in the finite case and it was generalized to finite pseudometric betweennesses by Beaudou et al. In this paper, we give a new, independent proof to the finite case of the original theorem which we reformulate in terms of linearity of betweenness structures.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Linearity ; Metric space ; Structural analysis</subject><ispartof>arXiv.org, 2020-05</ispartof><rights>2020. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>780,784</link.rule.ids></links><search><creatorcontrib>Szabó, Péter G N</creatorcontrib><title>A New Proof for the Characterization of Linear Betweenness Structure</title><title>arXiv.org</title><description>In their paper published in 1997, Richmond and Richmond classified metric spaces in which all triangles are degenerate. That result was later reproved by Dovgoshei and Dordovskii in the finite case and it was generalized to finite pseudometric betweennesses by Beaudou et al. In this paper, we give a new, independent proof to the finite case of the original theorem which we reformulate in terms of linearity of betweenness structures.</description><subject>Linearity</subject><subject>Metric space</subject><subject>Structural analysis</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNyrEKwjAQgOEgCBbtOxw4F2LStDpqVRxEBN1LKFfaIoleLhR8eh18AKd_-P6JSJTWq2ydKzUTaQiDlFIVpTJGJ2K_hQuOcCXvW2g9AXcIVWfJNozUvy333sHXzr1DS7BDHhGdwxDgxhQbjoQLMW3tI2D661wsj4d7dcqe5F8RA9eDj-S-VCtZmiIvtNno_64P-fA6Tw</recordid><startdate>20200531</startdate><enddate>20200531</enddate><creator>Szabó, Péter G N</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20200531</creationdate><title>A New Proof for the Characterization of Linear Betweenness Structure</title><author>Szabó, Péter G N</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20756463593</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Linearity</topic><topic>Metric space</topic><topic>Structural analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Szabó, Péter G N</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Szabó, Péter G N</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>A New Proof for the Characterization of Linear Betweenness Structure</atitle><jtitle>arXiv.org</jtitle><date>2020-05-31</date><risdate>2020</risdate><eissn>2331-8422</eissn><abstract>In their paper published in 1997, Richmond and Richmond classified metric spaces in which all triangles are degenerate. That result was later reproved by Dovgoshei and Dordovskii in the finite case and it was generalized to finite pseudometric betweennesses by Beaudou et al. In this paper, we give a new, independent proof to the finite case of the original theorem which we reformulate in terms of linearity of betweenness structures.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2020-05
issn 2331-8422
language eng
recordid cdi_proquest_journals_2075646359
source Free E- Journals
subjects Linearity
Metric space
Structural analysis
title A New Proof for the Characterization of Linear Betweenness Structure
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T13%3A42%3A11IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=A%20New%20Proof%20for%20the%20Characterization%20of%20Linear%20Betweenness%20Structure&rft.jtitle=arXiv.org&rft.au=Szab%C3%B3,%20P%C3%A9ter%20G%20N&rft.date=2020-05-31&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2075646359%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2075646359&rft_id=info:pmid/&rfr_iscdi=true