{"id":"https://openalex.org/W1975597184","doi":"https://doi.org/10.1016/s1571-0661(04)80952-6","title":"A Relationship between Equilogical Spaces and Type Two Effectivity","display_name":"A Relationship between Equilogical Spaces and Type Two Effectivity","publication_year":2001,"publication_date":"2001-11-01","ids":{"openalex":"https://openalex.org/W1975597184","doi":"https://doi.org/10.1016/s1571-0661(04)80952-6","mag":"1975597184"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(04)80952-6","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80952-6","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)80952-6","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068602858","display_name":"Andrej Bauer","orcid":"https://orcid.org/0000-0001-5378-0547"},"institutions":[{"id":"https://openalex.org/I1341284090","display_name":"Royal Swedish Academy of Sciences","ror":"https://ror.org/00j62qv07","country_code":"SE","type":"funder","lineage":["https://openalex.org/I1341284090"]},{"id":"https://openalex.org/I4210119493","display_name":"Mittag-Leffler Institute","ror":"https://ror.org/02z85gz67","country_code":"SE","type":"facility","lineage":["https://openalex.org/I1341284090","https://openalex.org/I4210119493"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Andrej Bauer","raw_affiliation_strings":["Institut Mittag-Leffler, The Royal Swedish Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Institut Mittag-Leffler, The Royal Swedish Academy of Sciences","institution_ids":["https://openalex.org/I4210119493","https://openalex.org/I1341284090"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068602858"],"corresponding_institution_ids":["https://openalex.org/I1341284090","https://openalex.org/I4210119493"],"apc_list":null,"apc_paid":null,"fwci":2.7277,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.90828254,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"45","issue":null,"first_page":"1","last_page":"21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9940999746322632,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/subcategory","display_name":"Subcategory","score":0.8732954859733582},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8237582445144653},{"id":"https://openalex.org/keywords/cartesian-closed-category","display_name":"Cartesian closed category","score":0.7789392471313477},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.7181604504585266},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5451450347900391},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5151547193527222},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.48176810145378113},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.4739508628845215},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46951574087142944},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.45896247029304504},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.43292197585105896},{"id":"https://openalex.org/keywords/baire-space","display_name":"Baire space","score":0.4268289804458618},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4251798093318939},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1404556930065155},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08329340815544128}],"concepts":[{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.8732954859733582},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8237582445144653},{"id":"https://openalex.org/C171032842","wikidata":"https://www.wikidata.org/wiki/Q1725874","display_name":"Cartesian closed category","level":2,"score":0.7789392471313477},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.7181604504585266},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5451450347900391},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5151547193527222},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.48176810145378113},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.4739508628845215},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46951574087142944},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.45896247029304504},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.43292197585105896},{"id":"https://openalex.org/C166359235","wikidata":"https://www.wikidata.org/wiki/Q1150180","display_name":"Baire space","level":2,"score":0.4268289804458618},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4251798093318939},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1404556930065155},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08329340815544128},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s1571-0661(04)80952-6","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80952-6","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:CiteSeerX.psu:10.1.1.24.2430","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.2430","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.cmu.edu/~andrej/papers/equ_and_tte.ps.gz","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(04)80952-6","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80952-6","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":[{"score":0.7099999785423279,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W104853290","https://openalex.org/W1497877209","https://openalex.org/W1525431708","https://openalex.org/W1547926009","https://openalex.org/W1552077134","https://openalex.org/W1595891412","https://openalex.org/W1605765292","https://openalex.org/W1606231391","https://openalex.org/W1719974439","https://openalex.org/W1966478469","https://openalex.org/W1986005496","https://openalex.org/W1995053131","https://openalex.org/W2031853948","https://openalex.org/W2045368155","https://openalex.org/W2069898398","https://openalex.org/W2168229531","https://openalex.org/W2330548796","https://openalex.org/W2468719830","https://openalex.org/W2611511037","https://openalex.org/W4213275635","https://openalex.org/W4244425465","https://openalex.org/W6632708164","https://openalex.org/W6636127056","https://openalex.org/W6658386821"],"related_works":["https://openalex.org/W2744653121","https://openalex.org/W2372920785","https://openalex.org/W2550443614","https://openalex.org/W4243341749","https://openalex.org/W2034974328","https://openalex.org/W3123970169","https://openalex.org/W2391207294","https://openalex.org/W2085318782","https://openalex.org/W1995053131","https://openalex.org/W1986005496"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"I":[3],"compare":[4],"two":[5,42],"well":[6],"studied":[7],"approaches":[8],"to":[9,57,73,195,203,209],"topological":[10,171],"semantics":[11,172],"\u2014":[12],"the":[13,18,32,82,124,164,188,192],"domain-theoretic":[14,165],"approach,":[15],"exemplified":[16,30],"by":[17,31],"category":[19,33],"of":[20,34,50,78,81,90,128,173],"countably":[21,51,160,180],"based":[22,52,161,181],"equilogical":[23],"spaces,":[24],"Equ,":[25,79],"and":[26,97,106,132,148,167,191],"Type":[27],"Two":[28],"Effectivity,":[29],"Baire":[35],"space":[36],"representations,":[37],"Rep(":[38,68,94,101,129,145],"B":[39,69,95,102,130,146],").":[40],"These":[41],"categories":[43],"are":[44,62,134],"both":[45],"locally":[46],"cartesian":[47,125,154],"closed":[48,126,155],"extensions":[49],"T0-spaces.":[53,162,182],"A":[54],"natural":[55,189],"question":[56],"ask":[58],"is":[59,71],"how":[60,197],"they":[61,114],"related.":[63],"First,":[64],"we":[65,142],"show":[66,143],"that":[67,123,144,157],")":[70,96,103,131,147],"equivalent":[72,170],"a":[74,88,139,152],"full":[75],"coreflective":[76],"subcategory":[77,156],"consisting":[80],"so-called":[83],"0-equilogical":[84],"spaces.":[85],"This":[86,121],"establishes":[87],"pair":[89],"adjoint":[91],"functors":[92],"between":[93],"Equ.":[98],"The":[99],"inclusion":[100],"\u2192":[104],"Equ":[105,133,149],"its":[107],"coreflection":[108],"have":[109],"many":[110],"desirable":[111],"properties,":[112],"but":[113],"do":[115,150],"not":[116],"preserve":[117],"exponentials":[118],"in":[119,138],"general.":[120],"means":[122],"structures":[127],"essentially":[135],"different.":[136],"However,":[137],"second":[140],"comparison":[141],"share":[151],"common":[153],"contains":[158],"all":[159,176],"Therefore,":[163],"approach":[166],"TTE":[168],"yield":[169],"computation":[174],"for":[175],"higher-order":[177],"types":[178],"over":[179],"We":[183],"consider":[184],"several":[185],"examples":[186],"involving":[187],"numbers":[190,194],"real":[193],"demonstrate":[196],"these":[198],"comparisons":[199],"make":[200],"it":[201],"possible":[202],"transfer":[204],"results":[205],"from":[206],"one":[207],"setting":[208],"another.":[210]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}