{"id":"https://openalex.org/W3013326781","doi":"https://doi.org/10.1016/j.topol.2026.109856","title":"An interpolation of metrics and spaces of metrics","display_name":"An interpolation of metrics and spaces of metrics","publication_year":2026,"publication_date":"2026-05-14","ids":{"openalex":"https://openalex.org/W3013326781","doi":"https://doi.org/10.1016/j.topol.2026.109856","mag":"3013326781"},"language":"en","primary_location":{"id":"doi:10.1016/j.topol.2026.109856","doi":"https://doi.org/10.1016/j.topol.2026.109856","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.topol.2026.109856","pdf_url":null,"source":{"id":"https://openalex.org/S20133105","display_name":"Topology and its Applications","issn_l":"0166-8641","issn":["0166-8641","1879-3207"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Topology and its Applications","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.topol.2026.109856","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072870097","display_name":"Yoshito Ishiki","orcid":"https://orcid.org/0009-0002-7792-8280","observed_orcids":["https://orcid.org/0009-0002-7792-8280"]},"institutions":[{"id":"https://openalex.org/I69740276","display_name":"Tokyo Metropolitan University","ror":"https://ror.org/00ws30h19","country_code":"JP","type":"education","lineage":["https://openalex.org/I69740276"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yoshito Ishiki","raw_affiliation_strings":["Department of Mathematical Sciences, Tokyo Metropolitan University, Minami-osawa Hachioji Tokyo 192-0397, Japan"],"raw_orcid":"https://orcid.org/0009-0002-7792-8280","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tokyo Metropolitan University, Minami-osawa Hachioji Tokyo 192-0397, Japan","institution_ids":["https://openalex.org/I69740276"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5072870097"],"corresponding_institution_ids":["https://openalex.org/I69740276"],"apc_list":{"value":2920,"currency":"USD","value_usd":2920},"apc_paid":{"value":2920,"currency":"USD","value_usd":2920},"fwci":6.5235,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.95101158,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"388","issue":null,"first_page":"109856","last_page":"109856"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9272000193595886,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9272000193595886,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.016699999570846558,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.012199999764561653,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metrizable-spaces","display_name":"metrizable spaces","score":0.8730000257492065},{"id":"https://openalex.org/keywords/closed-sets","display_name":"closed sets","score":0.8360000252723694},{"id":"https://openalex.org/keywords/density","display_name":"density","score":0.46399998664855957},{"id":"https://openalex.org/keywords/metric-geometry","display_name":"metric geometry","score":0.5899999737739563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7747783064842224},{"id":"https://openalex.org/C105433845","wikidata":"https://www.wikidata.org/wiki/Q1194053","display_name":"Metrization theorem","level":3,"score":0.7358872890472412},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6627097129821777},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.6385778188705444},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5769116878509521},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5661822557449341},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5400629043579102},{"id":"https://openalex.org/C191226916","wikidata":"https://www.wikidata.org/wiki/Q5384710","display_name":"Equivalence of metrics","level":4,"score":0.5138821601867676},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4977993965148926},{"id":"https://openalex.org/C154497576","wikidata":"https://www.wikidata.org/wiki/Q7247777","display_name":"Product metric","level":3,"score":0.43801435828208923},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3785948157310486},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21896249055862427},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19084754586219788},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11077553033828735},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.09410139918327332},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.057092905044555664},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/j.topol.2026.109856","doi":"https://doi.org/10.1016/j.topol.2026.109856","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.topol.2026.109856","pdf_url":null,"source":{"id":"https://openalex.org/S20133105","display_name":"Topology and its Applications","issn_l":"0166-8641","issn":["0166-8641","1879-3207"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Topology and its Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2003.13227","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.13227","pdf_url":"https://arxiv.org/pdf/2003.13227","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2003.13227","doi":"https://doi.org/10.48550/arxiv.2003.13227","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.13227","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1016/j.topol.2026.109856","doi":"https://doi.org/10.1016/j.topol.2026.109856","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.topol.2026.109856","pdf_url":null,"source":{"id":"https://openalex.org/S20133105","display_name":"Topology and its Applications","issn_l":"0166-8641","issn":["0166-8641","1879-3207"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Topology and its Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1489864335","display_name":null,"funder_award_id":"JP24KJ0182","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3876011062","display_name":"\u8ddd\u96e2\u7a7a\u9593\u306e\u64ec\u5bfe\u79f0\u6027\u3068\u5e7e\u4f55\u5b66\u7684\u6b21\u5143\u306e\u7814\u7a76","funder_award_id":"18J21300","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320326286","display_name":"Tokyo Metropolitan University","ror":"https://ror.org/00ws30h19"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3013326781.pdf","grobid_xml":"https://content.openalex.org/works/W3013326781.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W285160544","https://openalex.org/W590604990","https://openalex.org/W639877759","https://openalex.org/W745968820","https://openalex.org/W1016425580","https://openalex.org/W1523004878","https://openalex.org/W1549038146","https://openalex.org/W1580231046","https://openalex.org/W1671098680","https://openalex.org/W1817473158","https://openalex.org/W1989207698","https://openalex.org/W1996974722","https://openalex.org/W2016562424","https://openalex.org/W2028564333","https://openalex.org/W2064208474","https://openalex.org/W2075860643","https://openalex.org/W2087767893","https://openalex.org/W2099200243","https://openalex.org/W2322654430","https://openalex.org/W2332314867","https://openalex.org/W2760719516","https://openalex.org/W2982461000","https://openalex.org/W3103415653","https://openalex.org/W4231010334","https://openalex.org/W4234207164","https://openalex.org/W4238128467","https://openalex.org/W4252888111"],"related_works":["https://openalex.org/W7119322540","https://openalex.org/W7208461599","https://openalex.org/W2321756662","https://openalex.org/W3157410154","https://openalex.org/W1975913066","https://openalex.org/W4318305351","https://openalex.org/W2267670355","https://openalex.org/W2020452627","https://openalex.org/W7027278348","https://openalex.org/W4388875177"],"abstract_inverted_index":{"As":[0,26],"a":[1,15],"generalization":[2],"of":[3,7,14,17,23,32,34,37,44,56,63,77,84],"Hausdorff's":[4],"extension":[5],"theorem":[6,13],"metrics,":[8],"we":[9,29],"prove":[10],"an":[11,27],"interpolation":[12],"family":[16],"metrics":[18,46,64,80],"defined":[19],"on":[20,65],"closed":[21],"subsets":[22,33,60],"metrizable":[24,66],"spaces.":[25,67],"application,":[28],"investigate":[30],"typicality":[31],"moduli":[35],"spaces":[36,62],"metrics.":[38,88],"We":[39],"observe":[40],"that":[41],"various":[42],"sets":[43],"all":[45,78,85],"with":[47],"properties":[48],"appearing":[49],"in":[50,61],"metric":[51],"geometry":[52],"are":[53],"dense":[54],"intersections":[55],"countably":[57],"many":[58],"open":[59],"For":[68],"instance,":[69],"our":[70],"study":[71],"is":[72],"applicable":[73],"to":[74],"the":[75,82],"set":[76,83],"non-doubling":[79],"and":[81],"non-uniformly":[86],"disconnected":[87]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2020-04-03T00:00:00"}