{"id":"https://openalex.org/W1595955265","doi":"https://doi.org/10.1007/3-540-68535-9_22","title":"Approaches to Effective Semi-continuity of Real Functions","display_name":"Approaches to Effective Semi-continuity of Real Functions","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1595955265","doi":"https://doi.org/10.1007/3-540-68535-9_22","mag":"1595955265"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-68535-9_22","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-68535-9_22","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","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/A5019910641","display_name":"Vasco Brattka","orcid":"https://orcid.org/0000-0003-4664-2183"},"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":false,"raw_author_name":"Vasco Brattka","raw_affiliation_strings":["Theoretische Informatik I, FernUniversit\u00e4t Hagen, 58084, Hagen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Theoretische Informatik I, FernUniversit\u00e4t Hagen, 58084, Hagen, Germany","institution_ids":["https://openalex.org/I120691247"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050312341","display_name":"Klaus Weihrauch","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":false,"raw_author_name":"Klaus Weihrauch","raw_affiliation_strings":["Theoretische Informatik I, FernUniversit\u00e4t Hagen, 58084, Hagen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Theoretische Informatik I, FernUniversit\u00e4t Hagen, 58084, Hagen, Germany","institution_ids":["https://openalex.org/I120691247"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102089636","display_name":"Xizhong Zheng","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":false,"raw_author_name":"Xizhong Zheng","raw_affiliation_strings":["Theoretische Informatik I, FernUniversit\u00e4t Hagen, 58084, Hagen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Theoretische Informatik I, FernUniversit\u00e4t Hagen, 58084, Hagen, Germany","institution_ids":["https://openalex.org/I120691247"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I120691247"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"184","last_page":"193"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9812999963760376,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9714000225067139,"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/computability","display_name":"Computability","score":0.8894585371017456},{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.7338990569114685},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.723092794418335},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.7222169637680054},{"id":"https://openalex.org/keywords/epigraph","display_name":"Epigraph","score":0.6361292600631714},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5559059381484985},{"id":"https://openalex.org/keywords/real-valued-function","display_name":"Real-valued function","score":0.5386651754379272},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4873729348182678},{"id":"https://openalex.org/keywords/real-analysis","display_name":"Real analysis","score":0.4829920530319214},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43665021657943726},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.4317620098590851},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4145588278770447},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3485412001609802},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.334827721118927},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1420787274837494}],"concepts":[{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.8894585371017456},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.7338990569114685},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.723092794418335},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.7222169637680054},{"id":"https://openalex.org/C17192189","wikidata":"https://www.wikidata.org/wiki/Q1347059","display_name":"Epigraph","level":2,"score":0.6361292600631714},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5559059381484985},{"id":"https://openalex.org/C130231550","wikidata":"https://www.wikidata.org/wiki/Q5189500","display_name":"Real-valued function","level":2,"score":0.5386651754379272},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4873729348182678},{"id":"https://openalex.org/C1911482","wikidata":"https://www.wikidata.org/wiki/Q854531","display_name":"Real analysis","level":2,"score":0.4829920530319214},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43665021657943726},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.4317620098590851},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4145588278770447},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3485412001609802},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.334827721118927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1420787274837494},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-68535-9_22","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-68535-9_22","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W220096824","https://openalex.org/W561072077","https://openalex.org/W1497475168","https://openalex.org/W1546826212","https://openalex.org/W1587181421","https://openalex.org/W1597097264","https://openalex.org/W2095367910","https://openalex.org/W2117832390","https://openalex.org/W2157734704","https://openalex.org/W2905135108","https://openalex.org/W2912673661"],"related_works":["https://openalex.org/W197714092","https://openalex.org/W2527631632","https://openalex.org/W2150482238","https://openalex.org/W4249483016","https://openalex.org/W2295875602","https://openalex.org/W2962816983","https://openalex.org/W2046021909","https://openalex.org/W2158020605","https://openalex.org/W2147410830","https://openalex.org/W1595955265"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}