{"id":"https://openalex.org/W1544955410","doi":"https://doi.org/10.1007/3-540-44683-4_20","title":"Computable Versions of Baire\u2019s Category Theorem","display_name":"Computable Versions of Baire\u2019s Category Theorem","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1544955410","doi":"https://doi.org/10.1007/3-540-44683-4_20","mag":"1544955410"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-44683-4_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-44683-4_20","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":"book-chapter","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":"University of Hagen","ror":"https://ror.org/04tkkr536","country_code":"DE","type":"education","lineage":["https://openalex.org/I120691247"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Vasco Brattka","raw_affiliation_strings":["Theoretische Informatik I, Informatikzentrum, FernUniversit\u2019at, Hagen, Germany","FernUniversit\u2019at"],"affiliations":[{"raw_affiliation_string":"Theoretische Informatik I, Informatikzentrum, FernUniversit\u2019at, Hagen, Germany","institution_ids":["https://openalex.org/I120691247"]},{"raw_affiliation_string":"FernUniversit\u2019at","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019910641"],"corresponding_institution_ids":["https://openalex.org/I120691247"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.0892,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.85722892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"224","last_page":"235"},"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":0.9871000051498413,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9754999876022339,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.8698989152908325},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.683739185333252},{"id":"https://openalex.org/keywords/baire-category-theorem","display_name":"Baire category theorem","score":0.6584382653236389},{"id":"https://openalex.org/keywords/baire-space","display_name":"Baire space","score":0.5942758321762085},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5082840323448181},{"id":"https://openalex.org/keywords/gap-theorem","display_name":"Gap theorem","score":0.4992961883544922},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.47027355432510376},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.42379242181777954},{"id":"https://openalex.org/keywords/computable-number","display_name":"Computable number","score":0.4235232174396515},{"id":"https://openalex.org/keywords/baire-measure","display_name":"Baire measure","score":0.4150412380695343},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40873095393180847},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40109983086586},{"id":"https://openalex.org/keywords/compactness-theorem","display_name":"Compactness theorem","score":0.3937414884567261},{"id":"https://openalex.org/keywords/fundamental-theorem","display_name":"Fundamental theorem","score":0.38633695244789124},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3469906449317932},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.10527703166007996}],"concepts":[{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.8698989152908325},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.683739185333252},{"id":"https://openalex.org/C44659138","wikidata":"https://www.wikidata.org/wiki/Q1052678","display_name":"Baire category theorem","level":2,"score":0.6584382653236389},{"id":"https://openalex.org/C166359235","wikidata":"https://www.wikidata.org/wiki/Q1150180","display_name":"Baire space","level":2,"score":0.5942758321762085},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5082840323448181},{"id":"https://openalex.org/C3853638","wikidata":"https://www.wikidata.org/wiki/Q1314081","display_name":"Gap theorem","level":5,"score":0.4992961883544922},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.47027355432510376},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.42379242181777954},{"id":"https://openalex.org/C156382255","wikidata":"https://www.wikidata.org/wiki/Q818895","display_name":"Computable number","level":4,"score":0.4235232174396515},{"id":"https://openalex.org/C189892329","wikidata":"https://www.wikidata.org/wiki/Q2577940","display_name":"Baire measure","level":2,"score":0.4150412380695343},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40873095393180847},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40109983086586},{"id":"https://openalex.org/C171636804","wikidata":"https://www.wikidata.org/wiki/Q1149458","display_name":"Compactness theorem","level":4,"score":0.3937414884567261},{"id":"https://openalex.org/C194886279","wikidata":"https://www.wikidata.org/wiki/Q430271","display_name":"Fundamental theorem","level":3,"score":0.38633695244789124},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3469906449317932},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.10527703166007996}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/3-540-44683-4_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-44683-4_20","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.94.933","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.94.933","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.informatik.fernuni-hagen.de/thi1/vasco.brattka/publications/baire.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W623765668","https://openalex.org/W1497475168","https://openalex.org/W1509579779","https://openalex.org/W1545819195","https://openalex.org/W1590304156","https://openalex.org/W1595402987","https://openalex.org/W1967072078","https://openalex.org/W2005841729","https://openalex.org/W2077769760","https://openalex.org/W2574999163","https://openalex.org/W2611511037","https://openalex.org/W2864058903","https://openalex.org/W2912268883","https://openalex.org/W4243563333","https://openalex.org/W4244425465","https://openalex.org/W6619767332"],"related_works":["https://openalex.org/W2007775665","https://openalex.org/W1492946114","https://openalex.org/W1986579593","https://openalex.org/W1713431582","https://openalex.org/W2811297303","https://openalex.org/W1480530468","https://openalex.org/W1577501449","https://openalex.org/W2565599026","https://openalex.org/W1498085647","https://openalex.org/W2005943267"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}