{"id":"https://openalex.org/W7223265062","doi":"https://doi.org/10.48550/arxiv.2610.31059","title":"Topological preservation under aggregation of quantale-valued metric spaces","display_name":"Topological preservation under aggregation of quantale-valued metric spaces","publication_year":2026,"publication_date":"2026-10-22","ids":{"openalex":"https://openalex.org/W7223265062","doi":"https://doi.org/10.48550/arxiv.2610.31059"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.31059","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31059","pdf_url":"https://arxiv.org/pdf/2610.31059","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.31059","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5116463130","display_name":"Alejandro Fructuoso-Bonet","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fructuoso-Bonet, Alejandro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5159312625","display_name":"Jes\u00fas Rodr\\'\u0131guez-L\u00f3pez","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rodr\\'\u0131guez-L\u00f3pez, Jes\u00fas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9214000105857849,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9214000105857849,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.02539999969303608,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.016699999570846558,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/aggregation-operators","display_name":"aggregation operators","score":0.9929999709129333},{"id":"https://openalex.org/keywords/topology-preservation","display_name":"topology preservation","score":0.7820000052452087},{"id":"https://openalex.org/keywords/scott-continuity","display_name":"Scott continuity","score":0.9819999933242798},{"id":"https://openalex.org/keywords/upper-semicontinuity","display_name":"upper semicontinuity","score":0.8059999942779541},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.5540000200271606},{"id":"https://openalex.org/keywords/data-fusion","display_name":"data fusion","score":0.8360000252723694}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7541000247001648},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.6326000094413757},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5162000060081482},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.5095000267028809},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5090000033378601},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.47609999775886536},{"id":"https://openalex.org/C129089157","wikidata":"https://www.wikidata.org/wiki/Q621550","display_name":"General topology","level":3,"score":0.4521999955177307},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.438400000333786},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4124000072479248},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4090999960899353},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.4052000045776367},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.37950000166893005},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.37790000438690186},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3598000109195709},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3456000089645386},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C29585364","wikidata":"https://www.wikidata.org/wiki/Q1079166","display_name":"Domain theory","level":2,"score":0.2874999940395355}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.31059","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31059","pdf_url":"https://arxiv.org/pdf/2610.31059","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.2610.31059","doi":"https://doi.org/10.48550/arxiv.2610.31059","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.31059","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-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.31059","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31059","pdf_url":"https://arxiv.org/pdf/2610.31059","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":[{"id":"https://openalex.org/G410571670","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G451917667","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G5539308778","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G5967599077","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G9000361258","display_name":null,"funder_award_id":"PID2022-139248NB-I00","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"}],"funders":[{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":"https://ror.org/003x0zc53"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223265062.pdf","grobid_xml":"https://content.openalex.org/works/W7223265062.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7157909667","https://openalex.org/W4408986241","https://openalex.org/W7036019480","https://openalex.org/W3035639841","https://openalex.org/W4414458048","https://openalex.org/W4388895375","https://openalex.org/W2002993568","https://openalex.org/W4408055371","https://openalex.org/W2796600467","https://openalex.org/W2510936950"],"abstract_inverted_index":{"Aggregation":[0],"functions":[1,183,199,218],"provide":[2],"a":[3,11,16,67,89,155],"general":[4,180],"mechanism":[5],"for":[6,82,166,212],"combining":[7],"multiple":[8],"inputs":[9],"into":[10,103],"single":[12],"output":[13],"and":[14,74,106,109,141,169,171,196,203,215],"constitute":[15],"fundamental":[17],"tool":[18],"in":[19,133],"information":[20],"fusion.":[21],"Beyond":[22],"the":[23,33,39,48,54,62,84,121,124,136,139,142,147,179],"classical":[24],"numerical":[25],"setting,":[26],"aggregation":[27,55,198,217],"can":[28],"also":[29],"be":[30],"considered":[31],"at":[32,120],"level":[34],"of":[35,47,64,123,135,138,146,158,192],"mathematical":[36],"structures,":[37],"where":[38],"main":[40],"question":[41],"is":[42,115,131],"to":[43,117,182,187],"determine":[44],"which":[45,83],"properties":[46],"original":[49],"structures":[50],"are":[51],"preserved":[52],"by":[53,88],"process.":[56],"In":[57],"this":[58,101],"paper,":[59],"we":[60,153,177],"study":[61],"preservation":[63,114,130],"topology":[65,86],"within":[66],"unified":[68],"framework":[69],"based":[70],"on":[71,200,204,219],"continuous":[72],"quantales":[73],"quantale-enriched":[75],"categories.":[76],"We":[77,99],"introduce":[78],"strongly":[79,159,193],"preserving":[80,160],"functions,":[81,161],"natural":[85],"induced":[87,96],"$\\mathscr":[90,173],"V$-metric":[91,174],"space":[92],"coincides":[93],"with":[94,163,209],"that":[95,111],"after":[97],"aggregation.":[98],"decompose":[100],"property":[102],"its":[104],"upper":[105,112,144],"lower":[107,128],"versions":[108],"show":[110],"strong":[113,129],"equivalent":[116],"Scott":[118,143],"continuity":[119],"unit":[122,140],"domain":[125],"quantale,":[126],"whereas":[127],"characterized":[132],"terms":[134],"fibre":[137],"semicontinuity":[145],"inverse":[148],"multifunction.":[149],"Combining":[150],"these":[151],"results,":[152],"obtain":[154],"complete":[156],"characterization":[157],"together":[162,208],"analogous":[164],"results":[165,211],"separated,":[167],"symmetric,":[168],"separated":[170],"symmetric":[172],"spaces.":[175],"Finally,":[176],"specialize":[178],"theory":[181],"from":[184],"$\\mathsf":[185,188],"P_+^{\\,I}$":[186],"P_+$,":[189],"obtaining":[190],"characterizations":[191],"extended":[194,213],"quasi-pseudometric":[195],"pseudometric":[197],"Cartesian":[201,220],"products":[202],"common":[205],"underlying":[206],"sets,":[207],"corresponding":[210],"quasi-metric":[214],"metric":[216],"products.":[221]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-24T00:00:00"}