{"id":"https://openalex.org/W1995053131","doi":"https://doi.org/10.1016/s1571-0661(04)80084-7","title":"The Largest Topological Subcategory of Countably-based Equilogical Spaces","display_name":"The Largest Topological Subcategory of Countably-based Equilogical Spaces","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W1995053131","doi":"https://doi.org/10.1016/s1571-0661(04)80084-7","mag":"1995053131"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(04)80084-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80084-7","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1016/s1571-0661(04)80084-7","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113488559","display_name":"Mat\u0131\u0301as Menni","orcid":null},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Mat\u00edas Menni","raw_affiliation_strings":["Laboratory for Foundations of Computer Science, Division of Informatics, University of Edinburgh, Edinburgh, Scotland"],"affiliations":[{"raw_affiliation_string":"Laboratory for Foundations of Computer Science, Division of Informatics, University of Edinburgh, Edinburgh, Scotland","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110256373","display_name":"Alex Simpson","orcid":null},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alex Simpson","raw_affiliation_strings":["Laboratory for Foundations of Computer Science, Division of Informatics, University of Edinburgh, Edinburgh, Scotland"],"affiliations":[{"raw_affiliation_string":"Laboratory for Foundations of Computer Science, Division of Informatics, University of Edinburgh, Edinburgh, Scotland","institution_ids":["https://openalex.org/I98677209"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113488559"],"corresponding_institution_ids":["https://openalex.org/I98677209"],"apc_list":null,"apc_paid":null,"fwci":2.0642,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.84184463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":null,"first_page":"375","last_page":"398"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9965999722480774,"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/T10420","display_name":"Intracranial Aneurysms: Treatment and Complications","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2728","display_name":"Neurology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/subcategory","display_name":"Subcategory","score":0.9415383338928223},{"id":"https://openalex.org/keywords/cartesian-closed-category","display_name":"Cartesian closed category","score":0.7919585704803467},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.7846645712852478},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.760622501373291},{"id":"https://openalex.org/keywords/category-of-topological-spaces","display_name":"Category of topological spaces","score":0.7502937316894531},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5400482416152954},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5264742374420166},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5054922103881836},{"id":"https://openalex.org/keywords/concrete-category","display_name":"Concrete category","score":0.5018773078918457},{"id":"https://openalex.org/keywords/topological-vector-space","display_name":"Topological vector space","score":0.4817369282245636},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4672410786151886},{"id":"https://openalex.org/keywords/topological-tensor-product","display_name":"Topological tensor product","score":0.4574190676212311},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.4396120309829712},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3600320816040039},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1696791648864746},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1445738673210144},{"id":"https://openalex.org/keywords/functional-analysis","display_name":"Functional analysis","score":0.10964858531951904},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.08589878678321838},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06606242060661316}],"concepts":[{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.9415383338928223},{"id":"https://openalex.org/C171032842","wikidata":"https://www.wikidata.org/wiki/Q1725874","display_name":"Cartesian closed category","level":2,"score":0.7919585704803467},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.7846645712852478},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.760622501373291},{"id":"https://openalex.org/C83177873","wikidata":"https://www.wikidata.org/wiki/Q2000555","display_name":"Category of topological spaces","level":5,"score":0.7502937316894531},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5400482416152954},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5264742374420166},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5054922103881836},{"id":"https://openalex.org/C128520899","wikidata":"https://www.wikidata.org/wiki/Q1575634","display_name":"Concrete category","level":3,"score":0.5018773078918457},{"id":"https://openalex.org/C47776270","wikidata":"https://www.wikidata.org/wiki/Q1455249","display_name":"Topological vector space","level":3,"score":0.4817369282245636},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4672410786151886},{"id":"https://openalex.org/C178099376","wikidata":"https://www.wikidata.org/wiki/Q7825044","display_name":"Topological tensor product","level":4,"score":0.4574190676212311},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.4396120309829712},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3600320816040039},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1696791648864746},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1445738673210144},{"id":"https://openalex.org/C55112680","wikidata":"https://www.wikidata.org/wiki/Q190549","display_name":"Functional analysis","level":3,"score":0.10964858531951904},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.08589878678321838},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06606242060661316},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/s1571-0661(04)80084-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80084-7","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/bc5eeaae-4ba2-4f43-b4eb-830e4c9fbc4b","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/bc5eeaae-4ba2-4f43-b4eb-830e4c9fbc4b","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Menni, M & Simpson, A 1999, 'The Largest Topological Subcategory of Countably-based Equilogical Spaces', Electronic Notes in Theoretical Computer Science, vol. 20, no. 0, pp. 375 - 398. https://doi.org/10.1016/S1571-0661(04)80084-7","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.47.6134","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.6134","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dcs.ed.ac.uk/~als/Research/largest.ps.gz","raw_type":"text"},{"id":"pmh:oai:pure.ed.ac.uk:publications/bc5eeaae-4ba2-4f43-b4eb-830e4c9fbc4b","is_oa":true,"landing_page_url":"http://www.sciencedirect.com/science/article/pii/S1571066104800847","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(04)80084-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80084-7","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W29563611","https://openalex.org/W36563925","https://openalex.org/W124154939","https://openalex.org/W193353937","https://openalex.org/W1582269801","https://openalex.org/W1823042607","https://openalex.org/W1919166405","https://openalex.org/W1966478469","https://openalex.org/W1973559574","https://openalex.org/W1996443480","https://openalex.org/W2009311190","https://openalex.org/W2034290319","https://openalex.org/W2045614673","https://openalex.org/W2047996743","https://openalex.org/W2078095689","https://openalex.org/W2093541252","https://openalex.org/W2120713972","https://openalex.org/W2168229531","https://openalex.org/W2911635509","https://openalex.org/W3043060850","https://openalex.org/W4211265583","https://openalex.org/W4241603199","https://openalex.org/W4243711577","https://openalex.org/W6605083762","https://openalex.org/W6758708581","https://openalex.org/W6858954818"],"related_works":["https://openalex.org/W1986824257","https://openalex.org/W1995053131","https://openalex.org/W1986005496","https://openalex.org/W2075930735","https://openalex.org/W2386896477","https://openalex.org/W1533994011","https://openalex.org/W2374418299","https://openalex.org/W3123970169","https://openalex.org/W3014746455","https://openalex.org/W4249329088"],"abstract_inverted_index":{"There":[0],"are":[1,63],"two":[2,61],"main":[3],"approaches":[4,62],"to":[5,15,24,48],"obtaining":[6],"\u201ctopological\u201d":[7],"cartesian-closed":[8],"categories.":[9],"Under":[10,36],"one":[11,13,39,136],"approach,":[12],"restricts":[14],"a":[16,66,83,87,97],"full":[17,89,98],"subcategory":[18,90,99],"of":[19,33,43,51,69,77,100,106,111,141,151],"topological":[20,101,109,113],"spaces":[21,80],"that":[22,59,74,91,124],"happens":[23],"be":[25,93],"cartesian":[26,128],"closed":[27,129],"\u2014":[28,45],"for":[29,46,65],"example,":[30,47],"the":[31,37,41,60,75,135,139,146,149],"category":[32,76,104,126,140,150],"sequential":[34,142],"spaces.":[35,102,121,153],"other,":[38,147],"generalises":[40],"notion":[42,50],"space":[44],"Scott's":[49],"equilogical":[52,79,152],"space.":[53],"In":[54],"this":[55,125],"paper":[56],"we":[57],"show":[58,123],"equivalent":[64],"large":[67],"class":[68],"objects.":[70],"We":[71,122],"first":[72],"observe":[73],"countably-based":[78,112,120],"has,":[81],"in":[82,117],"precisely":[84],"defined":[85],"sense,":[86],"largest":[88],"can":[92],"simultaneously":[94],"viewed":[95],"as":[96],"This":[103],"consists":[105],"certain":[107],"\u201c\u03c9-projecting\u201d":[108],"quotients":[110],"spaces,":[114,143],"and":[115],"contains,":[116],"particular,":[118],"all":[119],"is":[127],"with":[130],"its":[131],"structure":[132],"inherited,":[133],"on":[134,145],"hand,":[137],"from":[138,148],"and,":[144]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}