Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces

Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces

We investigate the interrelations between labeled trees and ultrametric spaces generated by these trees. The labeled trees, which generate complete ultrametrics, totally bounded ultrametrics, and discrete ones, are characterized up to isomorphism. As corollary, we obtain a characterization of labele...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Annals of combinatorics 2022-09, Vol.26 (3), p.613-642
Hauptverfasser: Dovgoshey, Oleksiy, Küçükaslan, Mehmet
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Isomorphism
Mathematics
Mathematics and Statistics
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 642
container_issue 3
container_start_page 613
container_title Annals of combinatorics
container_volume 26
creator Dovgoshey, Oleksiy
Küçükaslan, Mehmet
description We investigate the interrelations between labeled trees and ultrametric spaces generated by these trees. The labeled trees, which generate complete ultrametrics, totally bounded ultrametrics, and discrete ones, are characterized up to isomorphism. As corollary, we obtain a characterization of labeled trees generating compact ultrametrics and discrete totally bounded ultrametrics. It is also shown that every ultrametric space generated by labeled tree contains a dense discrete subspace.
doi_str_mv 10.1007/s00026-022-00581-8
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2706755326</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2706755326</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-e3370926a3e1384a99b79bd8c8494728becbec757cea7fc64522f264a750fe453</originalsourceid><addsrcrecordid>eNp9UEtLAzEQDqJgffwBTwGvjU4eu0mOUrWKBQ-255BNZ8uW7W5Ntgf_vbEreBMG5mO-x8BHyA2HOw6g7xMAiJKBEAygMJyZEzIBwS2TYNXpEZtMQXlOLlLaZqRBigl5W_gKW1zTZURMdI4dRj803YbO-t2-xQGnR-TDMKW-W9PHJoWYz3TVDtHvcIhNoB-Zx3RFzmrfJrz-3Zdk9fy0nL2wxfv8dfawYEFyOzCUUoMVpZfIpVHe2krbam2CUVZpYSoMeXShA3pdh1IVQtSiVF4XUKMq5CW5HXP3sf88YBrctj_ELr90QkOpi0KKMqvEqAqxTyli7fax2fn45Ti4n9LcWJrLpbljac5kkxxNKYu7Dca_6H9c3zg-bfc</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2706755326</pqid></control><display><type>article</type><title>Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces</title><source>SpringerNature Journals</source><creator>Dovgoshey, Oleksiy ; Küçükaslan, Mehmet</creator><creatorcontrib>Dovgoshey, Oleksiy ; Küçükaslan, Mehmet</creatorcontrib><description>We investigate the interrelations between labeled trees and ultrametric spaces generated by these trees. The labeled trees, which generate complete ultrametrics, totally bounded ultrametrics, and discrete ones, are characterized up to isomorphism. As corollary, we obtain a characterization of labeled trees generating compact ultrametrics and discrete totally bounded ultrametrics. It is also shown that every ultrametric space generated by labeled tree contains a dense discrete subspace.</description><identifier>ISSN: 0218-0006</identifier><identifier>EISSN: 0219-3094</identifier><identifier>DOI: 10.1007/s00026-022-00581-8</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Combinatorics ; Isomorphism ; Mathematics ; Mathematics and Statistics</subject><ispartof>Annals of combinatorics, 2022-09, Vol.26 (3), p.613-642</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022</rights><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-e3370926a3e1384a99b79bd8c8494728becbec757cea7fc64522f264a750fe453</citedby><cites>FETCH-LOGICAL-c319t-e3370926a3e1384a99b79bd8c8494728becbec757cea7fc64522f264a750fe453</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00026-022-00581-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00026-022-00581-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Dovgoshey, Oleksiy</creatorcontrib><creatorcontrib>Küçükaslan, Mehmet</creatorcontrib><title>Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces</title><title>Annals of combinatorics</title><addtitle>Ann. Comb</addtitle><description>We investigate the interrelations between labeled trees and ultrametric spaces generated by these trees. The labeled trees, which generate complete ultrametrics, totally bounded ultrametrics, and discrete ones, are characterized up to isomorphism. As corollary, we obtain a characterization of labeled trees generating compact ultrametrics and discrete totally bounded ultrametrics. It is also shown that every ultrametric space generated by labeled tree contains a dense discrete subspace.</description><subject>Combinatorics</subject><subject>Isomorphism</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0218-0006</issn><issn>0219-3094</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9UEtLAzEQDqJgffwBTwGvjU4eu0mOUrWKBQ-255BNZ8uW7W5Ntgf_vbEreBMG5mO-x8BHyA2HOw6g7xMAiJKBEAygMJyZEzIBwS2TYNXpEZtMQXlOLlLaZqRBigl5W_gKW1zTZURMdI4dRj803YbO-t2-xQGnR-TDMKW-W9PHJoWYz3TVDtHvcIhNoB-Zx3RFzmrfJrz-3Zdk9fy0nL2wxfv8dfawYEFyOzCUUoMVpZfIpVHe2krbam2CUVZpYSoMeXShA3pdh1IVQtSiVF4XUKMq5CW5HXP3sf88YBrctj_ELr90QkOpi0KKMqvEqAqxTyli7fax2fn45Ti4n9LcWJrLpbljac5kkxxNKYu7Dca_6H9c3zg-bfc</recordid><startdate>20220901</startdate><enddate>20220901</enddate><creator>Dovgoshey, Oleksiy</creator><creator>Küçükaslan, Mehmet</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20220901</creationdate><title>Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces</title><author>Dovgoshey, Oleksiy ; Küçükaslan, Mehmet</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-e3370926a3e1384a99b79bd8c8494728becbec757cea7fc64522f264a750fe453</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Combinatorics</topic><topic>Isomorphism</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dovgoshey, Oleksiy</creatorcontrib><creatorcontrib>Küçükaslan, Mehmet</creatorcontrib><collection>CrossRef</collection><jtitle>Annals of combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dovgoshey, Oleksiy</au><au>Küçükaslan, Mehmet</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces</atitle><jtitle>Annals of combinatorics</jtitle><stitle>Ann. Comb</stitle><date>2022-09-01</date><risdate>2022</risdate><volume>26</volume><issue>3</issue><spage>613</spage><epage>642</epage><pages>613-642</pages><issn>0218-0006</issn><eissn>0219-3094</eissn><abstract>We investigate the interrelations between labeled trees and ultrametric spaces generated by these trees. The labeled trees, which generate complete ultrametrics, totally bounded ultrametrics, and discrete ones, are characterized up to isomorphism. As corollary, we obtain a characterization of labeled trees generating compact ultrametrics and discrete totally bounded ultrametrics. It is also shown that every ultrametric space generated by labeled tree contains a dense discrete subspace.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00026-022-00581-8</doi><tpages>30</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0218-0006
ispartof Annals of combinatorics, 2022-09, Vol.26 (3), p.613-642
issn 0218-0006
0219-3094
language eng
recordid cdi_proquest_journals_2706755326
source SpringerNature Journals
subjects Combinatorics
Isomorphism
Mathematics
Mathematics and Statistics
title Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T21%3A05%3A06IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Labeled%20Trees%20Generating%20Complete,%20Compact,%20and%20Discrete%20Ultrametric%20Spaces&rft.jtitle=Annals%20of%20combinatorics&rft.au=Dovgoshey,%20Oleksiy&rft.date=2022-09-01&rft.volume=26&rft.issue=3&rft.spage=613&rft.epage=642&rft.pages=613-642&rft.issn=0218-0006&rft.eissn=0219-3094&rft_id=info:doi/10.1007/s00026-022-00581-8&rft_dat=%3Cproquest_cross%3E2706755326%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2706755326&rft_id=info:pmid/&rfr_iscdi=true