{"id":"https://openalex.org/W7224135666","doi":"https://doi.org/10.48550/arxiv.2610.35912","title":"On families of copulas and quasi-copulas homeomorphic to the Hilbert cube and related results","display_name":"On families of copulas and quasi-copulas homeomorphic to the Hilbert cube and related results","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7224135666","doi":"https://doi.org/10.48550/arxiv.2610.35912"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.35912","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.35912","pdf_url":"https://arxiv.org/pdf/2610.35912","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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.35912","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071731167","display_name":"Fabrizio Durante","orcid":"https://orcid.org/0000-0002-4899-1080","observed_orcids":["https://orcid.org/0000-0002-4899-1080"]},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Durante, Fabrizio","raw_affiliation_strings":["Dipartimento di Matematica e Fisica \"Ennio De Giorgi\" , Universit\u00e0 del Salento , 73100 Lecce , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Fisica \"Ennio De Giorgi\" , Universit\u00e0 del Salento , 73100 Lecce , Italy","institution_ids":["https://openalex.org/I142910587"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160017432","display_name":"Juan Fern\u00e1ndez S\u00e1nchez","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S\u00e1nchez, Juan Fern\u00e1ndez","raw_affiliation_strings":["Almer\u00eda , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Almer\u00eda , Spain","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010888149","display_name":"Wolfgang Trutschnig","orcid":"https://orcid.org/0000-0002-7131-1944","observed_orcids":["https://orcid.org/0000-0002-7131-1944"]},"institutions":[{"id":"https://openalex.org/I182212641","display_name":"University of Salzburg","ror":"https://ror.org/05gs8cd61","country_code":"AT","type":"education","lineage":["https://openalex.org/I182212641"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Trutschnig, Wolfgang","raw_affiliation_strings":["Department for Artificial Intelligence and Human Interfaces , University of Salzburg , 5020 Salzburg , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department for Artificial Intelligence and Human Interfaces , University of Salzburg , 5020 Salzburg , Austria","institution_ids":["https://openalex.org/I182212641"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.5307999849319458,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.5307999849319458,"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":0.1460999995470047,"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"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.06069999933242798,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/copulas","display_name":"copulas","score":0.996999979019165},{"id":"https://openalex.org/keywords/quasi-copulas","display_name":"quasi-copulas","score":1.0},{"id":"https://openalex.org/keywords/hilbert-cube","display_name":"Hilbert cube","score":0.8989999890327454},{"id":"https://openalex.org/keywords/homeomorphism","display_name":"homeomorphism","score":0.8769999742507935},{"id":"https://openalex.org/keywords/z-sets","display_name":"Z-sets","score":0.8240000009536743},{"id":"https://openalex.org/keywords/fixed-point-property","display_name":"fixed point property","score":0.8180000185966492},{"id":"https://openalex.org/keywords/infinite-dimensional-topology","display_name":"infinite-dimensional topology","score":0.9359999895095825}],"concepts":[{"id":"https://openalex.org/C10728891","wikidata":"https://www.wikidata.org/wiki/Q584521","display_name":"Homeomorphism (graph theory)","level":2,"score":0.7669000029563904},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7333999872207642},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.657800018787384},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.5090000033378601},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48159998655319214},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4781999886035919},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4690000116825104},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.41749998927116394},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4138000011444092},{"id":"https://openalex.org/C174265945","wikidata":"https://www.wikidata.org/wiki/Q1142889","display_name":"Isolated point","level":4,"score":0.41290000081062317},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.40049999952316284},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39559999108314514},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.39250001311302185},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3898000121116638},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38769999146461487},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.38269999623298645},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36500000953674316},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3361999988555908},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C129089157","wikidata":"https://www.wikidata.org/wiki/Q621550","display_name":"General topology","level":3,"score":0.32269999384880066},{"id":"https://openalex.org/C17327563","wikidata":"https://www.wikidata.org/wiki/Q1991405","display_name":"Nowhere dense set","level":3,"score":0.32109999656677246},{"id":"https://openalex.org/C2991919592","wikidata":"https://www.wikidata.org/wiki/Q170058","display_name":"Continuous map","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C147493315","wikidata":"https://www.wikidata.org/wiki/Q3554824","display_name":"Hilbert manifold","level":3,"score":0.28110000491142273},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C105720234","wikidata":"https://www.wikidata.org/wiki/Q5456331","display_name":"Fixed-point property","level":3,"score":0.2590999901294708}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.35912","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.35912","pdf_url":"https://arxiv.org/pdf/2610.35912","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.2610.35912","doi":"https://doi.org/10.48550/arxiv.2610.35912","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.35912","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.35912","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.35912","pdf_url":"https://arxiv.org/pdf/2610.35912","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224135666.pdf","grobid_xml":"https://content.openalex.org/works/W7224135666.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4399379078","https://openalex.org/W4319593713","https://openalex.org/W4390278370","https://openalex.org/W2157755092","https://openalex.org/W2058065440","https://openalex.org/W1990426871","https://openalex.org/W7098880006","https://openalex.org/W2063803904","https://openalex.org/W2083163690","https://openalex.org/W2003824180"],"abstract_inverted_index":{"Working":[0,48],"with":[1,49],"tools":[2],"from":[3,19],"infinite-dimensional":[4],"topology":[5],"and":[6,17,35],"using":[7],"measure-theoretic":[8],"ideas":[9],"we":[10,52,81],"analyze":[11],"numerous":[12],"well-known":[13],"fami\\-lies":[14],"of":[15,26],"copu\\-las":[16],"quasi-copulas":[18],"a":[20,69,76,83,102],"topological":[21],"perspective,":[22],"prove":[23],"that":[24,68],"most":[25],"them":[27],"are":[28,100,111],"homeomorphic":[29],"to":[30,66,95,101],"the":[31,38,44],"Hilbert":[32],"cube":[33],"$\\mathcal{H}$":[34],"hence":[36],"have":[37],"Fixed":[39],"Point":[40],"as":[41,43],"well":[42],"Disjoint":[45],"Cells":[46],"property.":[47],"so-called":[50],"$Z$-sets,":[51],"then":[53],"study":[54],"how":[55],"large":[56],"one":[57],"set":[58,70],"is":[59,72],"within":[60,75],"another.":[61],"Doing":[62],"so,":[63],"in":[64],"order":[65],"show":[67],"$A$":[71],"small/topologically":[73],"negligible":[74],"compact":[77],"metric":[78],"space":[79],"$(\u03a9,m)$,":[80],"construct":[82],"homeomorphism":[84],"$h:":[85],"[0,1]":[86],"\\times":[87,93],"\\mathcal{H}":[88],"\\to":[89],"\u03a9$":[90],"mapping":[91],"$\\{0\\}":[92],"\\mathcal{H}$":[94],"$A$.":[96],"The":[97],"obtained":[98],"results":[99],"certain":[103],"extent":[104],"surprising":[105],"since":[106],"various":[107],"supposedly":[108],"small":[109],"families":[110],"topologically":[112],"large.":[113]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-10-29T00:00:00"}