{"id":"https://openalex.org/W7224889156","doi":"https://doi.org/10.48550/arxiv.2610.40381","title":"On the Converse of Shimoda's Theorem","display_name":"On the Converse of Shimoda's Theorem","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224889156","doi":"https://doi.org/10.48550/arxiv.2610.40381"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.40381","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40381","pdf_url":"https://arxiv.org/pdf/2610.40381","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/2610.40381","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160182759","display_name":"Sevdiyor Imomkulov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1302269238","display_name":"Academy of Sciences Republic of Uzbekistan","ror":"https://ror.org/01xgfaw76","country_code":"UZ","type":"government","lineage":["https://openalex.org/I1302269238","https://openalex.org/I4405266844"]},{"id":"https://openalex.org/I47151758","display_name":"National University of Uzbekistan","ror":"https://ror.org/011647w73","country_code":"UZ","type":"education","lineage":["https://openalex.org/I47151758"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Imomkulov, Sevdiyor","raw_affiliation_strings":["Department of Mathematical Analysis , National University of Uzbekistan named after Mirzo Ulugbek , University st. 14 , Tashkent , 100174 , Uzbekistan","V.I. Romanovkiy Institute of Mathematics , Academy of Sciences of Uzbekistan , University st. 9 , Tashkent , 100174 , Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Analysis , National University of Uzbekistan named after Mirzo Ulugbek , University st. 14 , Tashkent , 100174 , Uzbekistan","institution_ids":["https://openalex.org/I47151758"]},{"raw_affiliation_string":"V.I. Romanovkiy Institute of Mathematics , Academy of Sciences of Uzbekistan , University st. 9 , Tashkent , 100174 , Uzbekistan","institution_ids":["https://openalex.org/I1302269238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5118996917","display_name":"Rasulov Kamol","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405258343","display_name":"Tashkent University of Social Innovation","ror":"https://ror.org/00ggdkg91","country_code":"UZ","type":"education","lineage":["https://openalex.org/I4405258343"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Rasulov, Kamol","raw_affiliation_strings":["Department of Economics and Digital Technologies , Tashkent University of Social Innovation , Uzumzor st. 38 , Tashkent , 100015 , Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Economics and Digital Technologies , Tashkent University of Social Innovation , Uzumzor st. 38 , Tashkent , 100015 , Uzbekistan","institution_ids":["https://openalex.org/I4405258343"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.5278000235557556,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.5278000235557556,"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/T11822","display_name":"Analytic and geometric function theory","score":0.43849998712539673,"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/T12812","display_name":"Meromorphic and Entire Functions","score":0.00930000003427267,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/holomorphic-functions-of-several-complex-variables","display_name":"holomorphic functions of several complex variables","score":0.7910000085830688},{"id":"https://openalex.org/keywords/bidisc","display_name":"bidisc","score":0.9039999842643738},{"id":"https://openalex.org/keywords/converse-theorem","display_name":"converse theorem","score":0.4869999885559082},{"id":"https://openalex.org/keywords/nowhere-dense-sets","display_name":"nowhere dense sets","score":0.847000002861023},{"id":"https://openalex.org/keywords/holomorphic-extension","display_name":"holomorphic extension","score":0.6240000128746033},{"id":"https://openalex.org/keywords/countable-sets","display_name":"countable sets","score":0.43799999356269836},{"id":"https://openalex.org/keywords/domain-boundaries","display_name":"domain boundaries","score":0.3149999976158142}],"concepts":[{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.9071999788284302},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.861299991607666},{"id":"https://openalex.org/C45237699","wikidata":"https://www.wikidata.org/wiki/Q1038716","display_name":"Identity theorem","level":3,"score":0.7839999794960022},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.6762999892234802},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.6721000075340271},{"id":"https://openalex.org/C17327563","wikidata":"https://www.wikidata.org/wiki/Q1991405","display_name":"Nowhere dense set","level":3,"score":0.5794000029563904},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5116999745368958},{"id":"https://openalex.org/C42030387","wikidata":"https://www.wikidata.org/wiki/Q944297","display_name":"Open mapping theorem (functional analysis)","level":5,"score":0.4399999976158142},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.43309998512268066},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4142000079154968},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.36739999055862427},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.36739999055862427},{"id":"https://openalex.org/C11997311","wikidata":"https://www.wikidata.org/wiki/Q4751162","display_name":"Analyticity of holomorphic functions","level":4,"score":0.366100013256073},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.34459999203681946},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.32710000872612},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.32440000772476196},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.323199987411499},{"id":"https://openalex.org/C134618013","wikidata":"https://www.wikidata.org/wiki/Q518524","display_name":"Kakutani fixed-point theorem","level":5,"score":0.3125},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3052000105381012},{"id":"https://openalex.org/C51337361","wikidata":"https://www.wikidata.org/wiki/Q1825444","display_name":"Limit set","level":3,"score":0.29750001430511475},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.29510000348091125},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2842999994754791},{"id":"https://openalex.org/C90985795","wikidata":"https://www.wikidata.org/wiki/Q5042898","display_name":"Carlson's theorem","level":5,"score":0.2508000135421753},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.40381","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40381","pdf_url":"https://arxiv.org/pdf/2610.40381","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.2610.40381","doi":"https://doi.org/10.48550/arxiv.2610.40381","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.40381","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:2610.40381","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40381","pdf_url":"https://arxiv.org/pdf/2610.40381","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224889156.pdf","grobid_xml":"https://content.openalex.org/works/W7224889156.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4362636986","https://openalex.org/W2126181521","https://openalex.org/W1144300767","https://openalex.org/W7140174187","https://openalex.org/W353131830","https://openalex.org/W2087222955","https://openalex.org/W1968905466","https://openalex.org/W2043591566","https://openalex.org/W7099290332","https://openalex.org/W2022869879"],"abstract_inverted_index":{"We":[0,89],"study":[1],"Shimoda's":[2,117],"theorem":[3,118],"on":[4],"the":[5,114],"holomorphicity":[6],"of":[7,86,116,133],"a":[8,13,56,81,91,111],"function":[9,112],"$f(z,w)$":[10,73],"defined":[11],"in":[12,65,70,76,122],"bidisc":[14],"$U\\times":[15,77,87],"V=\\left\\{":[16],"\\left|":[17,22],"z":[18],"\\right|<1":[19,24],"\\right\\}\\times":[20],"\\left\\{":[21],"w":[23],"\\right\\},$":[25],"which":[26],"is":[27,40,55,74,107,120],"holomorphic":[28,41,75,121],"with":[29,42,59],"respect":[30,43],"to":[31,44,130],"$w\\in":[32,50],"V$":[33,54,78,125],"for":[34,47,80,93],"each":[35,48],"fixed":[36,49],"$z\\in":[37,45],"U$":[38,46,101],"and":[39,126],"E$,":[51],"where":[52],"$E\\subset":[53],"countable":[57],"set":[58,99],"at":[60],"least":[61],"one":[62],"limit":[63],"point":[64,132],"$V$.":[66],"Shimoda":[67],"proved":[68],"that":[69,103,119],"this":[71],"case":[72],"except":[79],"nowhere":[82,97],"dense":[83,98],"closed":[84,96],"subset":[85],"V$.":[88,135],"prove":[90],"converse:":[92],"any":[94,131],"relatively":[95],"$S\\subset":[100],"such":[102],"$\\partial":[104],"U\\bigcup":[105],"S$":[106],"connected,":[108],"there":[109],"exists":[110],"satisfying":[113],"conditions":[115],"$(U\\setminus":[123],"S)\\times":[124],"doesn't":[127],"extend":[128],"holomorphically":[129],"$S\\times":[134]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-10-31T00:00:00"}