{"id":"https://openalex.org/W1911952075","doi":"https://doi.org/10.3233/com-13009","title":"Weak K\u00f6nig\u2019s Lemma Implies the Uniform Continuity Theorem","display_name":"Weak K\u00f6nig\u2019s Lemma Implies the Uniform Continuity Theorem","publication_year":2013,"publication_date":"2013-02-01","ids":{"openalex":"https://openalex.org/W1911952075","doi":"https://doi.org/10.3233/com-13009","mag":"1911952075"},"language":"en","primary_location":{"id":"doi:10.3233/com-13009","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-13009","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086209658","display_name":"Hannes Diener","orcid":"https://orcid.org/0000-0002-1122-5753"},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Hannes Diener","raw_affiliation_strings":["University of Siegen, Germany, diener@math.uni-siegen.de"],"affiliations":[{"raw_affiliation_string":"University of Siegen, Germany, diener@math.uni-siegen.de","institution_ids":["https://openalex.org/I206895457"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086209658"],"corresponding_institution_ids":["https://openalex.org/I206895457"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.04886672,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2","issue":"1","first_page":"9","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9713000059127808,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9713000059127808,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9235000014305115,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.9189000129699707,"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/lemma","display_name":"Lemma (botany)","score":0.7224968075752258},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6655160784721375},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.46919533610343933},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3269256353378296}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7224968075752258},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6655160784721375},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46919533610343933},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3269256353378296},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/com-13009","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-13009","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.49000000953674316,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1979597421","https://openalex.org/W1097487277","https://openalex.org/W2007980826","https://openalex.org/W4285390085","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2768610039","https://openalex.org/W2061531152","https://openalex.org/W3002753104"],"abstract_inverted_index":{"As":[0],"the":[1,14,22],"title":[2],"suggests":[3],"we":[4],"are":[5],"going":[6],"to":[7,18],"show":[8],"that":[9],"Weak":[10],"K\u00f6nig\u2019s":[11],"Lemma":[12],"implies":[13],"uniform":[15,23],"continuity":[16,24],"theorem;":[17],"be":[19],"more":[20],"precise":[21],"theorem":[25],"for":[26,45],"functions":[27,46],"$[0,1]":[28,47],"\\to":[29,48],"\\R$":[30],".":[31,50],"This":[32],"improves":[33],"upon":[34],"a":[35],"result":[36],"by":[37],"J.":[38],"Berger":[39],"who":[40],"has":[41],"proven":[42],"this":[43],"implication":[44],"\\N$":[49]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
