{"id":"https://openalex.org/W4405964040","doi":"https://doi.org/10.2478/forma-2024-0011","title":"Ascoli-Arzel\u00e0 Theorem (Metric Space Version)","display_name":"Ascoli-Arzel\u00e0 Theorem (Metric Space Version)","publication_year":2024,"publication_date":"2024-08-01","ids":{"openalex":"https://openalex.org/W4405964040","doi":"https://doi.org/10.2478/forma-2024-0011"},"language":"en","primary_location":{"id":"doi:10.2478/forma-2024-0011","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2024-0011","pdf_url":"https://reference-global.com/2/v2/download/article/10.2478/forma-2024-0011.pdf","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://reference-global.com/2/v2/download/article/10.2478/forma-2024-0011.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030176832","display_name":"Keiichi Miyajima","orcid":null},"institutions":[{"id":"https://openalex.org/I6178835","display_name":"Ibaraki University","ror":"https://ror.org/00sjd5653","country_code":"JP","type":"education","lineage":["https://openalex.org/I6178835"]},{"id":"https://openalex.org/I65143321","display_name":"Hitachi (Japan)","ror":"https://ror.org/02exqgm79","country_code":"JP","type":"company","lineage":["https://openalex.org/I65143321"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Keiichi Miyajima","raw_affiliation_strings":["Ibaraki University, Faculty of Engineering Hitachi , Ibaraki , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ibaraki University, Faculty of Engineering Hitachi , Ibaraki , Japan","institution_ids":["https://openalex.org/I6178835","https://openalex.org/I65143321"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015411968","display_name":"Hiroshi Yamazaki","orcid":"https://orcid.org/0000-0001-9434-2957"},"institutions":[{"id":"https://openalex.org/I172086373","display_name":"Nagano Prefectural College","ror":"https://ror.org/03yp23s77","country_code":"JP","type":"education","lineage":["https://openalex.org/I172086373"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroshi Yamazaki","raw_affiliation_strings":["Nagano Prefectural Institute of Technology Nagano , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nagano Prefectural Institute of Technology Nagano , Japan","institution_ids":["https://openalex.org/I172086373"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17222023,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"32","issue":"1","first_page":"141","last_page":"147"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9696999788284302,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9696999788284302,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9386000037193298,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8081083297729492},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5500402450561523},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5287092924118042},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.45110052824020386},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4351266622543335},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42752742767333984},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.32073715329170227},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31229278445243835},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15406450629234314}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8081083297729492},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5500402450561523},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5287092924118042},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.45110052824020386},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4351266622543335},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42752742767333984},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32073715329170227},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31229278445243835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15406450629234314},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2478/forma-2024-0011","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2024-0011","pdf_url":"https://reference-global.com/2/v2/download/article/10.2478/forma-2024-0011.pdf","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/17772","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/17772","pdf_url":"https://repozytorium.uwb.edu.pl/jspui/bitstream/11320/17772/1/AscoliArzel-Theorem-Metric-Space-Version.pdf","source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/forma-2024-0011","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2024-0011","pdf_url":"https://reference-global.com/2/v2/download/article/10.2478/forma-2024-0011.pdf","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405964040.pdf","grobid_xml":"https://content.openalex.org/works/W4405964040.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1507925093","https://openalex.org/W2981188613","https://openalex.org/W3183811466","https://openalex.org/W4206292958","https://openalex.org/W4312973441"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1973641256","https://openalex.org/W2089274067","https://openalex.org/W56994397","https://openalex.org/W1121942432","https://openalex.org/W2418069309","https://openalex.org/W2376158287","https://openalex.org/W1526165314","https://openalex.org/W2959160600","https://openalex.org/W2359859943"],"abstract_inverted_index":{"Abstract":[0],"We":[1,25],"formulate":[2],"and":[3,13,31,36],"prove":[4],"in":[5],"Mizar":[6],"the":[7,27,32],"Ascoli-Arzel\u00e0\u2019s":[8],"theorem,":[9],"which":[10],"gives":[11],"necessary":[12],"sufficient":[14],"conditions":[15],"for":[16],"a":[17,39],"collection":[18],"of":[19,34,38,41],"continuous":[20,42],"functions":[21,43],"to":[22],"be":[23],"compact.":[24],"use":[26],"metric":[28],"space":[29],"setting,":[30],"notions":[33],"equicontinuousness":[35],"equiboundedness":[37],"set":[40],"are":[44],"utilized.":[45]},"counts_by_year":[],"updated_date":"2026-08-24T07:32:12.397491","created_date":"2025-10-10T00:00:00"}
