{"id":"https://openalex.org/W1978579553","doi":"https://doi.org/10.1007/s00224-004-1159-1","title":"Closure Properties of Real Number Classes underCBV Functions","display_name":"Closure Properties of Real Number Classes underCBV Functions","publication_year":2004,"publication_date":"2004-07-07","ids":{"openalex":"https://openalex.org/W1978579553","doi":"https://doi.org/10.1007/s00224-004-1159-1","mag":"1978579553"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-004-1159-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-004-1159-1","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"0025-5661","issn":["0025-5661","1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","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/A5102089636","display_name":"Xizhong Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]},{"id":"https://openalex.org/I51783024","display_name":"Brandenburg University of Technology Cottbus-Senftenberg","ror":"https://ror.org/02wxx3e24","country_code":"DE","type":"education","lineage":["https://openalex.org/I51783024"]}],"countries":["CN","DE"],"is_corresponding":false,"raw_author_name":"Xizhong Zheng","raw_affiliation_strings":["Department of Computer Science, Jiangsu University, Zhenjiang, Jiangsu, People's Republic of China","Theoretische Informatik, BTU Cottbus, 03044 Cottbus, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Jiangsu University, Zhenjiang, Jiangsu, People's Republic of China","institution_ids":["https://openalex.org/I115592961"]},{"raw_affiliation_string":"Theoretische Informatik, BTU Cottbus, 03044 Cottbus, Germany","institution_ids":["https://openalex.org/I51783024"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076334612","display_name":"Robert Rettinger","orcid":null},"institutions":[{"id":"https://openalex.org/I120691247","display_name":"FernUniversit\u00e4t in Hagen","ror":"https://ror.org/04tkkr536","country_code":"DE","type":"education","lineage":["https://openalex.org/I120691247"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Robert Rettinger","raw_affiliation_strings":["Theoretische Informatik II, FernUniversit\u00e4t Hagen, 58084 Hagen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Theoretische Informatik II, FernUniversit\u00e4t Hagen, 58084 Hagen, Germany","institution_ids":["https://openalex.org/I120691247"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030136295","display_name":"Romain Gengler","orcid":null},"institutions":[{"id":"https://openalex.org/I51783024","display_name":"Brandenburg University of Technology Cottbus-Senftenberg","ror":"https://ror.org/02wxx3e24","country_code":"DE","type":"education","lineage":["https://openalex.org/I51783024"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Romain Gengler","raw_affiliation_strings":["Theoretische Informatik, BTU Cottbus, 03044 Cottbus, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Theoretische Informatik, BTU Cottbus, 03044 Cottbus, Germany","institution_ids":["https://openalex.org/I51783024"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5076334612"],"corresponding_institution_ids":["https://openalex.org/I120691247"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":1.3737,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.79864238,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"6","first_page":"701","last_page":"729"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9854999780654907,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11567","display_name":"semigroups and automata theory","score":0.9696000218391418,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.787647545337677},{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.7631433010101318},{"id":"https://openalex.org/keywords/computable-number","display_name":"Computable number","score":0.7374268770217896},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6852976083755493},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.6761863231658936},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.6227850914001465},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6178761124610901},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4726856052875519},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4646576941013336},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.43736255168914795},{"id":"https://openalex.org/keywords/gap-theorem","display_name":"Gap theorem","score":0.43281614780426025},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4294391870498657},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2336462438106537},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1290816068649292},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05377975106239319}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.787647545337677},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.7631433010101318},{"id":"https://openalex.org/C156382255","wikidata":"https://www.wikidata.org/wiki/Q818895","display_name":"Computable number","level":4,"score":0.7374268770217896},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6852976083755493},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.6761863231658936},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.6227850914001465},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6178761124610901},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4726856052875519},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4646576941013336},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.43736255168914795},{"id":"https://openalex.org/C3853638","wikidata":"https://www.wikidata.org/wiki/Q1314081","display_name":"Gap theorem","level":5,"score":0.43281614780426025},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4294391870498657},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2336462438106537},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1290816068649292},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05377975106239319},{"id":"https://openalex.org/C81150689","wikidata":"https://www.wikidata.org/wiki/Q1217677","display_name":"Fundamental theorem of calculus","level":4,"score":0.0},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C206929604","wikidata":"https://www.wikidata.org/wiki/Q530152","display_name":"Picard\u2013Lindel\u00f6f theorem","level":3,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00224-004-1159-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-004-1159-1","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"0025-5661","issn":["0025-5661","1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W220096824","https://openalex.org/W623765668","https://openalex.org/W1486650289","https://openalex.org/W1497475168","https://openalex.org/W1509579779","https://openalex.org/W1542473208","https://openalex.org/W1545819195","https://openalex.org/W1552949294","https://openalex.org/W1562893243","https://openalex.org/W1577501449","https://openalex.org/W1980550011","https://openalex.org/W1994458535","https://openalex.org/W1997688386","https://openalex.org/W2007775665","https://openalex.org/W2008273724","https://openalex.org/W2024893387","https://openalex.org/W2037469541","https://openalex.org/W2056414301","https://openalex.org/W2093468014","https://openalex.org/W2118139375","https://openalex.org/W2150482238","https://openalex.org/W2397504689"],"related_works":["https://openalex.org/W2007775665","https://openalex.org/W1492946114","https://openalex.org/W2811297303","https://openalex.org/W1713431582","https://openalex.org/W1577501449","https://openalex.org/W2080359559","https://openalex.org/W1480530468","https://openalex.org/W2464649310","https://openalex.org/W153068418","https://openalex.org/W1498085647"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}