{"id":"https://openalex.org/W2081568593","doi":"https://doi.org/10.1155/2011/793848","title":"The Bolzano\u2010Poincar\u00e9 Type Theorems","display_name":"The Bolzano\u2010Poincar\u00e9 Type Theorems","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2081568593","doi":"https://doi.org/10.1155/2011/793848","mag":"2081568593"},"language":"en","primary_location":{"id":"doi:10.1155/2011/793848","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/793848","pdf_url":"http://downloads.hindawi.com/journals/ijmms/2011/793848.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/ijmms/2011/793848.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044451251","display_name":"Przemys\u0142aw Tkacz","orcid":"https://orcid.org/0000-0002-4166-7552"},"institutions":[{"id":"https://openalex.org/I69984877","display_name":"Cardinal Stefan Wyszynski University in Warsaw","ror":"https://ror.org/05sdyjv16","country_code":"PL","type":"education","lineage":["https://openalex.org/I69984877"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Przemys\u0142aw Tkacz","raw_affiliation_strings":["College of Science, Cardinal Stefan Wyszy\u0144ski, University in Warsaw, ul. Dewajtis 5, 01-815 Warszawa, Poland uw.edu.pl","College of Science, Cardinal Stefan Wyszy\u0144ski, University in Warsaw, ul. Dewajtis 5, 01-815 Warszawa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Cardinal Stefan Wyszy\u0144ski, University in Warsaw, ul. Dewajtis 5, 01-815 Warszawa, Poland uw.edu.pl","institution_ids":["https://openalex.org/I69984877"]},{"raw_affiliation_string":"College of Science, Cardinal Stefan Wyszy\u0144ski, University in Warsaw, ul. Dewajtis 5, 01-815 Warszawa","institution_ids":["https://openalex.org/I69984877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056458643","display_name":"Marian Turza\u0144ski","orcid":"https://orcid.org/0000-0002-3700-2558"},"institutions":[{"id":"https://openalex.org/I69984877","display_name":"Cardinal Stefan Wyszynski University in Warsaw","ror":"https://ror.org/05sdyjv16","country_code":"PL","type":"education","lineage":["https://openalex.org/I69984877"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Marian Turza\u0144ski","raw_affiliation_strings":["College of Science, Cardinal Stefan Wyszy\u0144ski, University in Warsaw, ul. Dewajtis 5, 01-815 Warszawa, Poland uw.edu.pl","College of Science, Cardinal Stefan Wyszy\u0144ski, University in Warsaw, ul. Dewajtis 5, 01-815 Warszawa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Cardinal Stefan Wyszy\u0144ski, University in Warsaw, ul. Dewajtis 5, 01-815 Warszawa, Poland uw.edu.pl","institution_ids":["https://openalex.org/I69984877"]},{"raw_affiliation_string":"College of Science, Cardinal Stefan Wyszy\u0144ski, University in Warsaw, ul. Dewajtis 5, 01-815 Warszawa","institution_ids":["https://openalex.org/I69984877"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056458643"],"corresponding_institution_ids":["https://openalex.org/I69984877"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.18447581,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2011","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9847999811172485,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T12170","display_name":"History and Theory of Mathematics","score":0.9847999811172485,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9699000120162964,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9279999732971191,"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/mathematics","display_name":"Mathematics","score":0.9175636768341064},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5759637355804443},{"id":"https://openalex.org/keywords/poincar\u00e9-conjecture","display_name":"Poincar\u00e9 conjecture","score":0.5636296272277832},{"id":"https://openalex.org/keywords/brouwer-fixed-point-theorem","display_name":"Brouwer fixed-point theorem","score":0.5047692060470581},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.469632625579834},{"id":"https://openalex.org/keywords/fundamental-theorem","display_name":"Fundamental theorem","score":0.4623841643333435},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4505331516265869},{"id":"https://openalex.org/keywords/polynomial-function-theorems-for-zeros","display_name":"Polynomial function theorems for zeros","score":0.4236105680465698},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.4188826084136963},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4102693200111389},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18632051348686218}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9175636768341064},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5759637355804443},{"id":"https://openalex.org/C88221313","wikidata":"https://www.wikidata.org/wiki/Q203586","display_name":"Poincar\u00e9 conjecture","level":2,"score":0.5636296272277832},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.5047692060470581},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.469632625579834},{"id":"https://openalex.org/C194886279","wikidata":"https://www.wikidata.org/wiki/Q430271","display_name":"Fundamental theorem","level":3,"score":0.4623841643333435},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4505331516265869},{"id":"https://openalex.org/C115115402","wikidata":"https://www.wikidata.org/wiki/Q12859399","display_name":"Polynomial function theorems for zeros","level":5,"score":0.4236105680465698},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.4188826084136963},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4102693200111389},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18632051348686218},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.0},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"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/C170412648","wikidata":"https://www.wikidata.org/wiki/Q4736415","display_name":"Alternating polynomial","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2011/793848","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/793848","pdf_url":"http://downloads.hindawi.com/journals/ijmms/2011/793848.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:793848","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2011/793848.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:cedc803f3ec04f4382e520207c81c771","is_oa":false,"landing_page_url":"https://doaj.org/article/cedc803f3ec04f4382e520207c81c771","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2011 (2011)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2011/793848","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/793848","pdf_url":"http://downloads.hindawi.com/journals/ijmms/2011/793848.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2081568593.pdf","grobid_xml":"https://content.openalex.org/works/W2081568593.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1984064613","https://openalex.org/W2259317415","https://openalex.org/W2318075236","https://openalex.org/W2602392563","https://openalex.org/W3140445122","https://openalex.org/W4210699733","https://openalex.org/W4302037145","https://openalex.org/W6736018645"],"related_works":["https://openalex.org/W3160581193","https://openalex.org/W175278553","https://openalex.org/W1891709587","https://openalex.org/W2086713333","https://openalex.org/W2063125267","https://openalex.org/W3170539842","https://openalex.org/W2016333943","https://openalex.org/W2093077775","https://openalex.org/W2357252996","https://openalex.org/W4241710913"],"abstract_inverted_index":{"In":[0,40,54],"1883\u20131884,":[1],"Henri":[2],"Poincar\u00e9":[3,47,59],"announced":[4],"the":[5,8,11,27,32,41,46,58,84,87,101,107,114],"result":[6],"about":[7],"structure":[9],"of":[10,13,15,29,31,74,83,89,100,109,116],"set":[12],"zeros":[14],"function":[16],"f":[17,34],":":[18],"I":[19],"n":[20,23,43,94],"\u2192":[21],"R":[22],",":[24],"or":[25],"alternatively":[26],"existence":[28,88,115],"solutions":[30],"equation":[33],"(":[35],"x":[36],")":[37],"=":[38,44,95],"0.":[39],"case":[42],"1":[45],"Theorem":[48,85,103],"is":[49,67,77],"well":[50],"known":[51],"Bolzano":[52],"Theorem.":[53,60],"1940":[55],"Miranda":[56],"rediscovered":[57],"Except":[61],"for":[62,93],"few":[63],"isolated":[64],"results":[65],"it":[66],"essentially":[68],"a":[69,90,117],"non\u2010algorithmic":[70],"theory.":[71],"The":[72],"aim":[73],"this":[75],"article":[76],"to":[78,105],"introduce":[79],"an":[80,97],"algorithmical":[81,98],"proof":[82,99],"\u201cOn":[86,113],"chain\u201d":[91,118],"and":[92,104,112],"3":[96],"Bolzano\u2010Poincar\u00e9":[102],"show":[106],"equivalence":[108],"Poincar\u00e9,":[110],"Brouwer":[111],"theorems.":[119]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}