{"id":"https://openalex.org/W1481505771","doi":"https://doi.org/10.4169/000298910x476031","title":"Variations on Kuratowski's 14-Set Theorem","display_name":"Variations on Kuratowski's 14-Set Theorem","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1481505771","doi":"https://doi.org/10.4169/000298910x476031","mag":"1481505771"},"language":"en","primary_location":{"id":"doi:10.4169/000298910x476031","is_oa":true,"landing_page_url":"https://doi.org/10.4169/000298910x476031","pdf_url":"https://www.tandfonline.com/doi/abs/10.4169/000298910X476031","source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.tandfonline.com/doi/abs/10.4169/000298910X476031","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082582740","display_name":"David K. Sherman","orcid":"https://orcid.org/0000-0003-4423-862X"},"institutions":[{"id":"https://openalex.org/I51556381","display_name":"University of Virginia","ror":"https://ror.org/0153tk833","country_code":"US","type":"education","lineage":["https://openalex.org/I51556381"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David Sherman","raw_affiliation_strings":["Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904-4137 dsherman@virginia.edu"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904-4137 dsherman@virginia.edu","institution_ids":["https://openalex.org/I51556381"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5082582740"],"corresponding_institution_ids":["https://openalex.org/I51556381"],"apc_list":null,"apc_paid":null,"fwci":2.0935,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.83562672,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"117","issue":"2","first_page":"113","last_page":"113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9828000068664551,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9828000068664551,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9797999858856201,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9575999975204468,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.5850351452827454},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5570286512374878},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.531751275062561},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4557154178619385},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3852832019329071},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37595033645629883},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35114026069641113},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28501230478286743},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2688602805137634},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2111283838748932},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.14793702960014343}],"concepts":[{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.5850351452827454},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5570286512374878},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.531751275062561},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4557154178619385},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3852832019329071},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37595033645629883},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35114026069641113},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28501230478286743},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2688602805137634},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2111283838748932},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.14793702960014343},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.4169/000298910x476031","is_oa":true,"landing_page_url":"https://doi.org/10.4169/000298910x476031","pdf_url":"https://www.tandfonline.com/doi/abs/10.4169/000298910X476031","source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.240.9454","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.240.9454","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/math/0405401v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.827.9413","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.827.9413","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.virginia.edu/%7Edes5e/papers/14-sets.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.4169/000298910x476031","is_oa":true,"landing_page_url":"https://doi.org/10.4169/000298910x476031","pdf_url":"https://www.tandfonline.com/doi/abs/10.4169/000298910X476031","source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1481505771.pdf","grobid_xml":"https://content.openalex.org/works/W1481505771.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W392721968","https://openalex.org/W959633836","https://openalex.org/W1500907847","https://openalex.org/W2050527500","https://openalex.org/W2078139873","https://openalex.org/W2312344490","https://openalex.org/W2320914512","https://openalex.org/W2324084724","https://openalex.org/W2587962973","https://openalex.org/W3127823229","https://openalex.org/W4213165878","https://openalex.org/W4250390189"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W2002282073","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878","https://openalex.org/W3212023493","https://openalex.org/W2790190308","https://openalex.org/W1991411408"],"abstract_inverted_index":{"Kuratowski's":[0],"14-set":[1],"theorem":[2],"says":[3],"that":[4],"in":[5],"a":[6,23],"topological":[7],"space,":[8],"14":[9],"is":[10],"the":[11,36,44,60],"maximum":[12],"possible":[13,41],"number":[14,53],"of":[15,43,54],"distinct":[16],"sets":[17],"which":[18],"can":[19],"be":[20],"generated":[21],"from":[22],"fixed":[24],"set":[25],"by":[26],"taking":[27],"closures":[28],"and":[29,51],"complements.":[30],"In":[31],"this":[32],"article":[33],"we":[34],"consider":[35],"analogous":[37],"questions":[38],"for":[39],"any":[40,52],"subcollection":[42],"operations":[45],"{closure,":[46],"complement,":[47],"interior,":[48],"intersection,":[49],"union},":[50],"initially":[55],"given":[56],"sets.":[57],"We":[58],"use":[59],"algebraic":[61],"\"topological":[62],"calculus\"":[63],"to":[64],"full":[65],"advantage.":[66]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"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":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}