{"id":"https://openalex.org/W1813666868","doi":"https://doi.org/10.2168/lmcs-10(4:16)2014","title":"Bounded variation and the strength of Helly's selection theorem","display_name":"Bounded variation and the strength of Helly's selection theorem","publication_year":2014,"publication_date":"2014-12-24","ids":{"openalex":"https://openalex.org/W1813666868","doi":"https://doi.org/10.2168/lmcs-10(4:16)2014","mag":"1813666868"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-10(4:16)2014","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-10(4:16)2014","pdf_url":"https://lmcs.episciences.org/980/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/980/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080684787","display_name":"Alexander Kreuzer","orcid":null},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Alexander P. Kreuzer","raw_affiliation_strings":["National University of Singapore"],"affiliations":[{"raw_affiliation_string":"National University of Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080684787"],"corresponding_institution_ids":["https://openalex.org/I165932596"],"apc_list":null,"apc_paid":null,"fwci":0.3656,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.60414395,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"Volume 10, Issue 4","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9984999895095825,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9934999942779541,"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/mathematics","display_name":"Mathematics","score":0.7642349600791931},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6684122085571289},{"id":"https://openalex.org/keywords/bounded-variation","display_name":"Bounded variation","score":0.6587828993797302},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6256858110427856},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5769528746604919},{"id":"https://openalex.org/keywords/variation","display_name":"Variation (astronomy)","score":0.53275465965271},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5060800909996033},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4832761883735657},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4333771765232086},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42046108841896057},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3301718533039093},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1622888743877411},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12239846587181091}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7642349600791931},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6684122085571289},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.6587828993797302},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6256858110427856},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5769528746604919},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.53275465965271},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5060800909996033},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4832761883735657},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4333771765232086},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42046108841896057},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3301718533039093},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1622888743877411},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12239846587181091},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2168/lmcs-10(4:16)2014","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-10(4:16)2014","pdf_url":"https://lmcs.episciences.org/980/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1308.3881","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1308.3881","pdf_url":"https://arxiv.org/pdf/1308.3881","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.764.7709","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.764.7709","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1308.3881.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:65c0fcf1462c4394ace5cfbbe3040f89","is_oa":true,"landing_page_url":"https://doaj.org/article/65c0fcf1462c4394ace5cfbbe3040f89","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 10, Issue 4 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-10(4:16)2014","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-10(4:16)2014","pdf_url":"https://lmcs.episciences.org/980/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1813666868.pdf","grobid_xml":"https://content.openalex.org/works/W1813666868.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1480714962","https://openalex.org/W1545863051","https://openalex.org/W1561006452","https://openalex.org/W1769462986","https://openalex.org/W2003539498","https://openalex.org/W2018837422","https://openalex.org/W2028509288","https://openalex.org/W2059834295","https://openalex.org/W2150482238","https://openalex.org/W2159347965","https://openalex.org/W2595348797","https://openalex.org/W3104977456","https://openalex.org/W3105905549","https://openalex.org/W3123382730","https://openalex.org/W3124326917"],"related_works":["https://openalex.org/W1977876013","https://openalex.org/W2057361304","https://openalex.org/W2389758888","https://openalex.org/W1485170658","https://openalex.org/W4243686829","https://openalex.org/W2801649141","https://openalex.org/W4301380664","https://openalex.org/W2057115809","https://openalex.org/W2051435915","https://openalex.org/W2963377212"],"abstract_inverted_index":{"We":[0,49],"analyze":[1],"the":[2,11,17,38,57,77],"strength":[3],"of":[4,19,21,31],"Helly's":[5],"selection":[6],"theorem":[7,15],"HST,":[8],"which":[9],"is":[10,53,65,74],"most":[12],"important":[13],"compactness":[14],"on":[16],"space":[18,33,40],"functions":[20],"bounded":[22],"variation.":[23],"For":[24],"this":[25,32,63],"we":[26],"utilize":[27],"a":[28],"new":[29],"representation":[30],"intermediate":[34],"between":[35],"$L_1$":[36],"and":[37],"Sobolev":[39],"W1,1,":[41],"compatible":[42],"with":[43],"the,":[44],"so":[45],"called,":[46],"weak*":[47],"topology.":[48],"obtain":[50],"that":[51],"HST":[52,64],"instance-wise":[54],"equivalent":[55,66],"to":[56,67],"Bolzano-Weierstra\\ss\\":[58],"principle":[59],"over":[60,69],"RCA0.":[61,70],"With":[62],"ACA0":[68],"A":[71],"similar":[72],"classification":[73],"obtained":[75],"in":[76],"Weihrauch":[78],"lattice.":[79]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}