{"id":"https://openalex.org/W4327526020","doi":"https://doi.org/10.1007/s10485-025-09844-w","title":"On Vector Spaces with Formal Infinite Sums","display_name":"On Vector Spaces with Formal Infinite Sums","publication_year":2026,"publication_date":"2026-03-04","ids":{"openalex":"https://openalex.org/W4327526020","doi":"https://doi.org/10.1007/s10485-025-09844-w"},"language":"en","primary_location":{"id":"doi:10.1007/s10485-025-09844-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-025-09844-w","pdf_url":null,"source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s10485-025-09844-w","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077439469","display_name":"Pietro Freni","orcid":null},"institutions":[{"id":"https://openalex.org/I202391551","display_name":"Czech Academy of Sciences","ror":"https://ror.org/053avzc18","country_code":"CZ","type":"government","lineage":["https://openalex.org/I202391551"]},{"id":"https://openalex.org/I4210100529","display_name":"Czech Academy of Sciences, Institute of Sociology","ror":"https://ror.org/018hy5194","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210100529"]},{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Pietro Freni","raw_affiliation_strings":["Institute of Mathematics, Czech Academy of Sciences, 110 00, Prague, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Czech Academy of Sciences, 110 00, Prague, Czech Republic","institution_ids":["https://openalex.org/I202391551","https://openalex.org/I4210100529","https://openalex.org/I4210120266"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5077439469"],"corresponding_institution_ids":["https://openalex.org/I202391551","https://openalex.org/I4210100529","https://openalex.org/I4210120266"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01840426,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.957099974155426,"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"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.957099974155426,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9517999887466431,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.932699978351593,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/mathematics","display_name":"Mathematics","score":0.627371072769165},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.5378028750419617},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5285771489143372},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.509292721748352},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.49143970012664795},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.4527743458747864},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4397450089454651},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.4201134741306305},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4187389314174652},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.4133950471878052},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39357665181159973},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32400140166282654},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19338086247444153},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11826115846633911},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1018100380897522}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.627371072769165},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.5378028750419617},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5285771489143372},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.509292721748352},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.49143970012664795},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.4527743458747864},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4397450089454651},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.4201134741306305},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4187389314174652},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.4133950471878052},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39357665181159973},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32400140166282654},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19338086247444153},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11826115846633911},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1018100380897522},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10485-025-09844-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-025-09844-w","pdf_url":null,"source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2303.08000","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2303.08000","pdf_url":"https://arxiv.org/pdf/2303.08000","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,"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":"pmh:doi:10.48550/arxiv.2303.08000","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2303.08000","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2303.08000","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1007/s10485-025-09844-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-025-09844-w","pdf_url":null,"source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4399999976158142,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1595870841","https://openalex.org/W3120288839","https://openalex.org/W1948188044","https://openalex.org/W1578654632","https://openalex.org/W2028193261","https://openalex.org/W4233444413","https://openalex.org/W1966101132","https://openalex.org/W2041531262","https://openalex.org/W1988612426","https://openalex.org/W2076508310","https://openalex.org/W2328260500","https://openalex.org/W2047241331","https://openalex.org/W2079655821","https://openalex.org/W3015933616","https://openalex.org/W2056361918","https://openalex.org/W4248828294","https://openalex.org/W3015451400","https://openalex.org/W3114375010","https://openalex.org/W2030227845","https://openalex.org/W1969046746","https://openalex.org/W4220765671","https://openalex.org/W1996952564","https://openalex.org/W4249001812"],"related_works":["https://openalex.org/W3100286349","https://openalex.org/W2896134808","https://openalex.org/W4289378085","https://openalex.org/W4294291164","https://openalex.org/W3172436493","https://openalex.org/W1887135636","https://openalex.org/W4287164812","https://openalex.org/W2386063599","https://openalex.org/W1975884855","https://openalex.org/W3213150849"],"abstract_inverted_index":{"Abstract":[0],"I":[1,37,47,115,120,149,186,239],"discuss":[2],"possible":[3,57],"definitions":[4],"of":[5,7,14,22,33,42,66,72,87,91,103,128,163,174,211,217,222,232,235],"categories":[6,41],"vector":[8,44,62,165],"spaces":[9,45,131,166,178],"enriched":[10],"with":[11,144,206,241],"a":[12,51,60,67,112,228],"notion":[13],"formal":[15,24,145],"infinite":[16,25,146],"linear":[17,26],"combination":[18],"in":[19,30,50,97,134],"the":[20,23,31,54,85,88,92,98,104,109,126,160,171,188,197,209,214,223],"likes":[21],"combinations":[27],"one":[28,199],"has":[29],"context":[32],"generalized":[34],"power":[35,102],"series,":[36],"call":[38,116],"these":[39,107],"reasonable":[40],"strong":[43,61,164],"(r.c.s.v.s.).":[46],"show":[48,121],"that,":[49],"precise":[52],"sense,":[53],"more":[55,229],"general":[56,230],"definition":[58],"for":[59,78,111],"space":[63],"is":[64,75,123],"that":[65,74,179,242],"small":[68],"$$\\textrm{Vect}$$":[69,73],"-enriched":[70],"endofunctor":[71],"right":[76],"orthogonal":[77,233],"every":[79],"cardinal":[80],"$$\\lambda":[81,93,99],"$$":[82,94,100],",":[83],"to":[84,125,153,158,170,208,227],"cokernel":[86],"canonical":[89],"inclusion":[90],"-th":[95,101],"copower":[96],"identity":[105],"functor:":[106],"form":[108],"objects":[110],"universal":[113],"r.c.s.v.s.":[114,172,194],"$$\\Sigma":[117],"\\textrm{Vect}$$":[118,168],".":[119,203,220],"this":[122,151],"equivalent":[124],"category":[127,152,162],"ultrafinite":[129],"summability":[130],"defined":[132],"independently":[133],"Bagayoko":[135],"et":[136],"al.":[137],"(Automorphisms":[138],"and":[139,169,238],"derivations":[140],"on":[141,192,200],"algebras":[142],"endowed":[143],"sums,":[147],"2024).":[148],"relate":[150],"what":[154],"could":[155],"be":[156,159],"understood":[157],"obvious":[161],"$$B\\Sigma":[167],"$$K\\textrm{TVect}_s$$":[173],"separated":[175],"linearly":[176,183],"topologized":[177],"are":[180],"generated":[181],"by":[182,196],"compact":[184],"spaces.":[185],"analyze":[187],"monoidal":[189],"closed":[190],"structures":[191],"various":[193],"induced":[195],"natural":[198],"$$\\textrm{Ind}{\\text":[201,218,236],"{-}}(\\textrm{Vect}^\\textrm{op})$$":[202,219,237],"In":[204],"particular":[205],"respect":[207],"problem":[210],"closure":[212],"under":[213],"tensor":[215],"product":[216],"Most":[221],"technical":[224],"results":[225],"apply":[226],"class":[231],"subcategories":[234],"work":[240],"generality":[243],"as":[244],"it\u2019s":[245],"cost-free.":[246]},"counts_by_year":[],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2023-03-17T00:00:00"}