{"id":"https://openalex.org/W1583458798","doi":"https://doi.org/10.3217/jucs-008-03-0382","title":"Some Notes on Fine Computability","display_name":"Some Notes on Fine Computability","publication_year":2020,"publication_date":"2020-04-07","ids":{"openalex":"https://openalex.org/W1583458798","doi":"https://doi.org/10.3217/jucs-008-03-0382","mag":"1583458798"},"language":"en","primary_location":{"id":"pmh:oai:zenodo.org:6996147","is_oa":true,"landing_page_url":"https://zenodo.org/record/6996147","pdf_url":"https://zenodo.org/record/6996147","source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"JUCS - Journal of Universal Computer Science 8((3)) 382-395","raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://zenodo.org/record/6996147","any_repository_has_fulltext":true},"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":["University of Hagen"],"affiliations":[{"raw_affiliation_string":"University of Hagen","institution_ids":["https://openalex.org/I120691247"]}]}],"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":null,"apc_paid":null,"fwci":0.2888,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.59394405,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"8","issue":null,"first_page":"382","last_page":"395"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":1.0,"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":1.0,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9767000079154968,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.7326833605766296},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.7157832384109497},{"id":"https://openalex.org/keywords/computable-number","display_name":"Computable number","score":0.6233882904052734},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6071441769599915},{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.6029164791107178},{"id":"https://openalex.org/keywords/unit-interval","display_name":"Unit interval","score":0.5733599662780762},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.549021303653717},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5464746356010437},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5462905168533325},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.49988341331481934},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.4876955449581146},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.44618433713912964},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4433250427246094},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4218725562095642},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.37952256202697754},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37787020206451416},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37759289145469666},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3209954500198364},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.2789901793003082},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16271820664405823},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08039331436157227}],"concepts":[{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.7326833605766296},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.7157832384109497},{"id":"https://openalex.org/C156382255","wikidata":"https://www.wikidata.org/wiki/Q818895","display_name":"Computable number","level":4,"score":0.6233882904052734},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6071441769599915},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.6029164791107178},{"id":"https://openalex.org/C128394911","wikidata":"https://www.wikidata.org/wiki/Q1987578","display_name":"Unit interval","level":2,"score":0.5733599662780762},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.549021303653717},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5464746356010437},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5462905168533325},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.49988341331481934},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4876955449581146},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.44618433713912964},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4433250427246094},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4218725562095642},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.37952256202697754},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37787020206451416},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37759289145469666},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3209954500198364},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2789901793003082},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16271820664405823},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08039331436157227},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:zenodo.org:6996147","is_oa":true,"landing_page_url":"https://zenodo.org/record/6996147","pdf_url":"https://zenodo.org/record/6996147","source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"JUCS - Journal of Universal Computer Science 8((3)) 382-395","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.100.990","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.100.990","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.jucs.org/jucs_8_3/some_notes_on_fine/Brattka_V.pdf","raw_type":"text"},{"id":"doi:10.3217/jucs-008-03-0382","is_oa":true,"landing_page_url":"https://doi.org/10.3217/jucs-008-03-0382","pdf_url":null,"source":{"id":"https://openalex.org/S4306400660","display_name":"TUGraz OPEN Library (Graz University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4092182","host_organization_name":"Graz University of Technology","host_organization_lineage":["https://openalex.org/I4092182"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:1583458798","is_oa":false,"landing_page_url":"https://www.jucs.org/jucs_8_3/some_notes_on_fine/Brattka_V.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S58563349","display_name":"JUCS - Journal of Universal Computer Science","issn_l":"0948-695X","issn":["0948-695X","0948-6968"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317875","host_organization_name":"Verlag der Technischen Universit\u00e4t Graz","host_organization_lineage":["https://openalex.org/P4310317875"],"host_organization_lineage_names":["Verlag der Technischen Universit\u00e4t Graz"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"JUCS - Journal of Universal Computer Science","raw_type":null}],"best_oa_location":{"id":"pmh:oai:zenodo.org:6996147","is_oa":true,"landing_page_url":"https://zenodo.org/record/6996147","pdf_url":"https://zenodo.org/record/6996147","source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"JUCS - Journal of Universal Computer Science 8((3)) 382-395","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"score":0.44999998807907104,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1583458798.pdf","grobid_xml":"https://content.openalex.org/works/W1583458798.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W86370709","https://openalex.org/W1537234249","https://openalex.org/W1602845793","https://openalex.org/W2005841729","https://openalex.org/W2025476736","https://openalex.org/W2047923539","https://openalex.org/W2049131802","https://openalex.org/W2076223733","https://openalex.org/W2611511037","https://openalex.org/W2911572548"],"related_works":["https://openalex.org/W2049131802","https://openalex.org/W30191827","https://openalex.org/W2035463901","https://openalex.org/W1497475168","https://openalex.org/W2010762030","https://openalex.org/W1522981711","https://openalex.org/W2398530055","https://openalex.org/W2313560776","https://openalex.org/W1585480578","https://openalex.org/W2998820293","https://openalex.org/W2964101234","https://openalex.org/W3034042404","https://openalex.org/W2076358125","https://openalex.org/W2113953702","https://openalex.org/W1983131597","https://openalex.org/W2011851191","https://openalex.org/W2963436468","https://openalex.org/W2052872633","https://openalex.org/W3085466727","https://openalex.org/W3044083951"],"abstract_inverted_index":{"A":[0],"metric":[1],"defined":[2,76],"by":[3,77],"Fine":[4,37,59,73,114],"induces":[5],"a":[6,35,46,55],"topology":[7,20],"on":[8,110],"the":[9,17,40,68,99,107,111],"unit":[10],"interval":[11],"which":[12,22,48,93],"is":[13,117],"strictly":[14],"stronger":[15],"than":[16],"ordinary":[18,85],"Euclidean":[19,101],"and":[21,43,62],"has":[23],"some":[24,90],"interesting":[25],"applications":[26],"in":[27],"Walsh":[28],"analysis.":[29],"We":[30],"investigate":[31],"computability":[32],"properties":[33],"of":[34,39,58,70,81,113],"corresponding":[36],"representation":[38],"real":[41],"numbers":[42],"we":[44,53,63,104],"construct":[45],"structure":[47],"characterizes":[49],"this":[50,65],"representation.":[51],"Moreover,":[52],"introduce":[54],"general":[56],"class":[57,66,69],"computable":[60,74,86],"functions":[61,75,82,87,92,116],"compare":[64],"with":[67,96],"locally":[71],"uniformly":[72],"Mori.":[78],"Both":[79],"classes":[80],"include":[83],"all":[84],"and,":[88],"additionally,":[89],"important":[91],"are":[94],"discontinuous":[95],"respect":[97],"to":[98],"usual":[100],"metric.":[102],"Finally,":[103],"prove":[105],"that":[106],"integration":[108],"operator":[109],"space":[112],"continuous":[115],"lower":[118],"semi-computable.":[119]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}