{"id":"https://openalex.org/W1547007913","doi":"https://doi.org/10.1002/malq.201200076","title":"From Bolzano\u2010Weierstra\u00df to Arzel\u00e0\u2010Ascoli","display_name":"From Bolzano\u2010Weierstra\u00df to Arzel\u00e0\u2010Ascoli","publication_year":2014,"publication_date":"2014-05-01","ids":{"openalex":"https://openalex.org/W1547007913","doi":"https://doi.org/10.1002/malq.201200076","mag":"1547007913"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201200076","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.201200076","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.201200076","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.201200076","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Alexander P. Kreuzer","orcid":null},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I4210144566","display_name":"Laboratoire de l'Informatique du Parall\u00e9lisme","ror":"https://ror.org/04msnz457","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210144566"]},{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]}],"countries":["FR","SG"],"is_corresponding":true,"raw_author_name":"Alexander P. Kreuzer","raw_affiliation_strings":["Department of Mathematics Faculty of Science National University of Singapore  Block S17, 10 Lower Kent Ridge Road, Singapore 119076 Singapore","Laboratoire de l'Informatique du Parall\u00e9lisme (LIP) \u00c9cole Normale Sup\u00e9rieure de Lyon  46\u00a0All\u00e9e d'Italie, 69364 Lyon Cedex 07 France"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Faculty of Science National University of Singapore  Block S17, 10 Lower Kent Ridge Road, Singapore 119076 Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"Laboratoire de l'Informatique du Parall\u00e9lisme (LIP) \u00c9cole Normale Sup\u00e9rieure de Lyon  46\u00a0All\u00e9e d'Italie, 69364 Lyon Cedex 07 France","institution_ids":["https://openalex.org/I4210144566","https://openalex.org/I113428412"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I113428412","https://openalex.org/I165932596","https://openalex.org/I4210144566"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05347304,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"60","issue":"3","first_page":"177","last_page":"183"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12812","display_name":"Meromorphic and Entire Functions","score":0.22030000388622284,"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/T12812","display_name":"Meromorphic and Entire Functions","score":0.22030000388622284,"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/T12508","display_name":"Functional Equations Stability Results","score":0.1396999955177307,"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":0.08009999990463257,"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/subsequence","display_name":"Subsequence","score":0.9221000075340271},{"id":"https://openalex.org/keywords/equicontinuity","display_name":"Equicontinuity","score":0.7630000114440918},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.7166000008583069},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6270999908447266},{"id":"https://openalex.org/keywords/longest-increasing-subsequence","display_name":"Longest increasing subsequence","score":0.3815999925136566},{"id":"https://openalex.org/keywords/arzel\u00e0\u2013ascoli-theorem","display_name":"Arzel\u00e0\u2013Ascoli theorem","score":0.3147999942302704}],"concepts":[{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.9221000075340271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8314999938011169},{"id":"https://openalex.org/C182539199","wikidata":"https://www.wikidata.org/wiki/Q249092","display_name":"Equicontinuity","level":2,"score":0.7630000114440918},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.7166000008583069},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6270999908447266},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3898000121116638},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38449999690055847},{"id":"https://openalex.org/C170006305","wikidata":"https://www.wikidata.org/wiki/Q4183855","display_name":"Longest increasing subsequence","level":4,"score":0.3815999925136566},{"id":"https://openalex.org/C197451259","wikidata":"https://www.wikidata.org/wiki/Q1477053","display_name":"Arzel\u00e0\u2013Ascoli theorem","level":5,"score":0.3147999942302704},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3118000030517578},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C129301229","wikidata":"https://www.wikidata.org/wiki/Q741865","display_name":"Uniform continuity","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C171636804","wikidata":"https://www.wikidata.org/wiki/Q1149458","display_name":"Compactness theorem","level":4,"score":0.2549999952316284},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25060001015663147}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/malq.201200076","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.201200076","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.201200076","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1205.5429","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1205.5429","pdf_url":"https://arxiv.org/pdf/1205.5429","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"}],"best_oa_location":{"id":"doi:10.1002/malq.201200076","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.201200076","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.201200076","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1547007913.pdf","grobid_xml":"https://content.openalex.org/works/W1547007913.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1973337017","https://openalex.org/W1979207178","https://openalex.org/W1998461400","https://openalex.org/W2018837422","https://openalex.org/W2069207426","https://openalex.org/W2106260240","https://openalex.org/W2148962283","https://openalex.org/W2154952077","https://openalex.org/W2949253467"],"related_works":[],"abstract_inverted_index":{"We":[0,83],"show":[1,84,115],"how":[2],"one":[3],"can":[4,21],"obtain":[5,27],"solutions":[6],"to":[7,91,102,106],"the":[8,15,23,31,36,46,61,66,92,107,118],"Arzel\u00e0\u2010Ascoli":[9,37],"theorem":[10,38],"using":[11],"suitable":[12],"applications":[13],"of":[14,30,33,35,42,52],"Bolzano\u2010Weierstra\u00df":[16,93],"principle.":[17],"With":[18],"this,":[19],"we":[20,114],"apply":[22],"results":[24],"from":[25],"and":[26,39,63,95,104,121],"a":[28,40,55,73],"classification":[29],"strength":[32],"instances":[34],"variant":[41],"it.":[43],"Let":[44],"be":[45,65],"statement":[47,67],"that":[48,57,68,85,96,116],"each":[49,69],"equicontinuous":[50],"sequence":[51,71],"functions":[53],"contains":[54,72],"subsequence":[56,74],"converges":[58,76],"uniformly":[59,77],"with":[60],"rate":[62],"let":[64],"such":[70],"which":[75],"but":[78],"possibly":[79],"without":[80],"any":[81],"rate.":[82],"is":[86,97],"instance\u2010wise":[87,98],"equivalent,":[88,99],"over":[89,100,117],",":[90,101,103,120],"principle":[94,110],"thus":[105],"strong":[108],"cohesive":[109],"(":[111],").":[112],"Moreover,":[113],"principles":[119],"are":[122],"equivalent.":[123]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2016-06-24T00:00:00"}
