{"id":"https://openalex.org/W1995109821","doi":"https://doi.org/10.1017/s0960129506005184","title":"Quotients of countably based spaces are not closed under sobrification","display_name":"Quotients of countably based spaces are not closed under sobrification","publication_year":2006,"publication_date":"2006-04-01","ids":{"openalex":"https://openalex.org/W1995109821","doi":"https://doi.org/10.1017/s0960129506005184","mag":"1995109821"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129506005184","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129506005184","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","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/A5028941231","display_name":"Gary Gruenhage","orcid":"https://orcid.org/0000-0001-8754-6775"},"institutions":[{"id":"https://openalex.org/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"GARY GRUENHAGE","raw_affiliation_strings":["Department of Mathematics, Auburn University, Auburn, AL 36849-5310, U.S.A","Department of Mathematics Auburn University Auburn, AL 36849-5310, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Auburn University, Auburn, AL 36849-5310, U.S.A","institution_ids":["https://openalex.org/I82497590"]},{"raw_affiliation_string":"Department of Mathematics Auburn University Auburn, AL 36849-5310, U.S.A","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022583176","display_name":"Thomas Streicher","orcid":"https://orcid.org/0000-0001-6725-0168"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technical University of Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"THOMAS STREICHER","raw_affiliation_strings":["Fachbereich Mathematik, Technische Universit\u00e4t Darmstadt, Schlo\u00dfgartenstr. 7, 64289 Darmstadt, Germany","Fachbereich Mathematik, Technische Universit\u00e4t Darmstadt, Schlo\u00dfgartenstr. 7, 64289 Darmstadt, Germany.#TAB#"],"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, Technische Universit\u00e4t Darmstadt, Schlo\u00dfgartenstr. 7, 64289 Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]},{"raw_affiliation_string":"Fachbereich Mathematik, Technische Universit\u00e4t Darmstadt, Schlo\u00dfgartenstr. 7, 64289 Darmstadt, Germany.#TAB#","institution_ids":["https://openalex.org/I31512782"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028941231"],"corresponding_institution_ids":["https://openalex.org/I82497590"],"apc_list":null,"apc_paid":null,"fwci":2.4264,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8743011,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"16","issue":"2","first_page":"223","last_page":"229"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9988999962806702,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9970999956130981,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9836999773979187,"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/counterexample","display_name":"Counterexample","score":0.7943028211593628},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7411412000656128},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.6430504322052002},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.6128041744232178},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.607020914554596},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.588532567024231},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.4148421287536621},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40164268016815186},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.33411145210266113},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17939063906669617},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14602237939834595},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.053368330001831055},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.042143940925598145}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7943028211593628},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7411412000656128},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6430504322052002},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.6128041744232178},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.607020914554596},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.588532567024231},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.4148421287536621},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40164268016815186},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.33411145210266113},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17939063906669617},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14602237939834595},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.053368330001831055},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.042143940925598145}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0960129506005184","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129506005184","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:tubiblio.ulb.tu-darmstadt.de:28139","is_oa":false,"landing_page_url":"http://tubiblio.ulb.tu-darmstadt.de/28139/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196390","display_name":"TUbilio (Technical University of Darmstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31512782","host_organization_name":"Technische Universit\u00e4t Darmstadt","host_organization_lineage":["https://openalex.org/I31512782"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.800000011920929,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W87343669","https://openalex.org/W1512577908","https://openalex.org/W1973559574","https://openalex.org/W1986005496","https://openalex.org/W2069246348","https://openalex.org/W2112131178","https://openalex.org/W2149175915","https://openalex.org/W2150223832","https://openalex.org/W2322118446"],"related_works":["https://openalex.org/W2319356426","https://openalex.org/W2963803326","https://openalex.org/W2963456550","https://openalex.org/W4248038692","https://openalex.org/W4249580765","https://openalex.org/W1506668851","https://openalex.org/W2087561891","https://openalex.org/W2094335718","https://openalex.org/W2093102607","https://openalex.org/W4367694328"],"abstract_inverted_index":{"In":[0],"this":[1],"note":[2],"we":[3],"show":[4],"that":[5,39,53],"quotients":[6],"of":[7,59,73],"countably":[8],"based":[9],"spaces":[10],"(qcb":[11],"spaces)":[12],"and":[13,21],"topological":[14,33],"predomains,":[15],"as":[16],"introduced":[17],"by":[18,47],"M.":[19],"Schr\u00f6der":[20],"A.":[22],"Simpson,":[23],"are":[24],"not":[25,36,45],"closed":[26],"under":[27],"sobrification.":[28,48],"As":[29],"a":[30,54],"consequence,":[31],"replete":[32],"predomains":[34],"need":[35],"be":[37],"sober,":[38],"is,":[40],"in":[41],"general,":[42],"repletion":[43,60],"is":[44],"given":[46],"Our":[49],"counterexample":[50],"also":[51,66],"shows":[52],"certain":[55],"tentative":[56],"\u2018equaliser":[57],"construction\u2019":[58],"fails":[61],"for":[62],"qcb":[63],"spaces.Our":[64],"results":[65],"extend":[67],"to":[68],"the":[69],"more":[70],"general":[71],"class":[72],"core":[74],"compactly":[75],"generated":[76],"spaces.":[77]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}