{"id":"https://openalex.org/W2335935258","doi":"https://doi.org/10.1007/s10485-016-9434-2","title":"Irreducible Equivalence Relations, Gleason Spaces, and de Vries Duality","display_name":"Irreducible Equivalence Relations, Gleason Spaces, and de Vries Duality","publication_year":2016,"publication_date":"2016-04-20","ids":{"openalex":"https://openalex.org/W2335935258","doi":"https://doi.org/10.1007/s10485-016-9434-2","mag":"2335935258"},"language":"en","primary_location":{"id":"doi:10.1007/s10485-016-9434-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-016-9434-2","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10485-016-9434-2.pdf","source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs10485-016-9434-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031772210","display_name":"Guram Bezhanishvili","orcid":null},"institutions":[{"id":"https://openalex.org/I10052268","display_name":"New Mexico State University","ror":"https://ror.org/00hpz7z43","country_code":"US","type":"education","lineage":["https://openalex.org/I10052268"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guram Bezhanishvili","raw_affiliation_strings":["Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003, USA","institution_ids":["https://openalex.org/I10052268"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045687469","display_name":"Nick Bezhanishvili","orcid":"https://orcid.org/0009-0005-6692-5051"},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Nick Bezhanishvili","raw_affiliation_strings":["Institute for Logic, Language and Computation, University of Amsterdam, P.O. BOX 94242, 1090, GE, Amsterdam, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Institute for Logic, Language and Computation, University of Amsterdam, P.O. BOX 94242, 1090, GE, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I887064364"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048515647","display_name":"Sumit Sourabh","orcid":"https://orcid.org/0000-0003-4559-0991"},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Sumit Sourabh","raw_affiliation_strings":["Institute for Logic, Language and Computation, University of Amsterdam, P.O. BOX 94242, 1090, GE, Amsterdam, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Institute for Logic, Language and Computation, University of Amsterdam, P.O. BOX 94242, 1090, GE, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I887064364"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105920523","display_name":"Yde Venema","orcid":null},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Yde Venema","raw_affiliation_strings":["Institute for Logic, Language and Computation, University of Amsterdam, P.O. BOX 94242, 1090, GE, Amsterdam, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Institute for Logic, Language and Computation, University of Amsterdam, P.O. BOX 94242, 1090, GE, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I887064364"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5045687469"],"corresponding_institution_ids":["https://openalex.org/I887064364"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.807,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.86084997,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"25","issue":"3","first_page":"381","last_page":"401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9987000226974487,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9987000226974487,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9921000003814697,"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":0.9797999858856201,"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":0.8401319980621338},{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.8258793354034424},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.5985615253448486},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5956209301948547},{"id":"https://openalex.org/keywords/urysohn-and-completely-hausdorff-spaces","display_name":"Urysohn and completely Hausdorff spaces","score":0.5601889491081238},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5281962156295776},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.485563725233078},{"id":"https://openalex.org/keywords/locally-compact-space","display_name":"Locally compact space","score":0.45705151557922363},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4381650686264038},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32083356380462646},{"id":"https://openalex.org/keywords/hausdorff-measure","display_name":"Hausdorff measure","score":0.1640203893184662},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.13342592120170593}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8401319980621338},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.8258793354034424},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.5985615253448486},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5956209301948547},{"id":"https://openalex.org/C84496893","wikidata":"https://www.wikidata.org/wiki/Q1135782","display_name":"Urysohn and completely Hausdorff spaces","level":4,"score":0.5601889491081238},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5281962156295776},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.485563725233078},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.45705151557922363},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4381650686264038},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32083356380462646},{"id":"https://openalex.org/C73225184","wikidata":"https://www.wikidata.org/wiki/Q1591095","display_name":"Hausdorff measure","level":3,"score":0.1640203893184662},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.13342592120170593},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10485-016-9434-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-016-9434-2","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10485-016-9434-2.pdf","source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},{"id":"pmh:oai:dare.uva.nl:openaire/aaa33759-d23f-40cf-b8c8-94b1fad47261","is_oa":true,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/irreducible-equivalence-relations-gleason-spaces-and-de-vries-duality(aaa33759-d23f-40cf-b8c8-94b1fad47261).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bezhanishvili, G, Bezhanishvili, N, Sourabh, S & Venema, Y 2017, 'Irreducible equivalence relations, Gleason spaces, and de Vries duality', Applied Categorical Structures, vol. 25, no. 3, pp. 381-401. https://doi.org/10.1007/s10485-016-9434-2","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/aaa33759-d23f-40cf-b8c8-94b1fad47261","is_oa":true,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/irreducible-equivalence-relations-gleason-spaces-and-de-vries-duality(aaa33759-d23f-40cf-b8c8-94b1fad47261).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bezhanishvili, G, Bezhanishvili, N, Sourabh, S & Venema, Y 2017, 'Irreducible equivalence relations, Gleason spaces, and de Vries duality', Applied Categorical Structures, vol. 25, no. 3, pp. 381-401. https://doi.org/10.1007/s10485-016-9434-2","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s10485-016-9434-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-016-9434-2","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10485-016-9434-2.pdf","source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2335935258.pdf","grobid_xml":"https://content.openalex.org/works/W2335935258.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W15321835","https://openalex.org/W190083431","https://openalex.org/W1543749070","https://openalex.org/W1547584114","https://openalex.org/W1581138540","https://openalex.org/W1603162778","https://openalex.org/W1991748341","https://openalex.org/W1992205482","https://openalex.org/W2007384104","https://openalex.org/W2014830113","https://openalex.org/W2017096836","https://openalex.org/W2022860141","https://openalex.org/W2026901353","https://openalex.org/W2029645949","https://openalex.org/W2054275301","https://openalex.org/W2061686800","https://openalex.org/W2114303461","https://openalex.org/W2120713972","https://openalex.org/W2145852765","https://openalex.org/W2286396437","https://openalex.org/W2315064349","https://openalex.org/W2315614361","https://openalex.org/W2529311106","https://openalex.org/W2610670723","https://openalex.org/W2785885914","https://openalex.org/W2963436654","https://openalex.org/W4211144022","https://openalex.org/W6646537399"],"related_works":["https://openalex.org/W1566340293","https://openalex.org/W3153358937","https://openalex.org/W1565490267","https://openalex.org/W2164191541","https://openalex.org/W2052460933","https://openalex.org/W4322717215","https://openalex.org/W2293913165","https://openalex.org/W2321187507","https://openalex.org/W2005225659","https://openalex.org/W4213436606"],"abstract_inverted_index":{"By":[0],"de":[1,17,92],"Vries":[2,18,93],"duality,":[3],"the":[4,14,36,70,78,89],"category":[5,15,71,79,90],"of":[6,16,38,72,80,91],"compact":[7,53,81],"Hausdorff":[8,54,82],"spaces":[9,74],"is":[10,43,49,58,75,85],"dually":[11,86],"equivalent":[12,76,87],"to":[13,77,88],"algebras":[19,22],"(complete":[20],"Boolean":[21],"endowed":[23],"with":[24],"a":[25,39,44],"proximity-like":[26],"relation).":[27],"We":[28],"provide":[29],"an":[30,50,59],"alternative":[31],"\u201cmodal-like\u201d":[32],"duality":[33],"by":[34],"introducing":[35],"concept":[37],"Gleason":[40,73],"space,":[41],"which":[42],"pair":[45],"(X,R),":[46],"where":[47],"X":[48],"extremally":[51],"disconnected":[52],"space":[55],"and":[56,84],"R":[57],"irreducible":[60],"equivalence":[61],"relation":[62],"on":[63],"X.":[64],"Our":[65],"main":[66],"result":[67],"states":[68],"that":[69],"spaces,":[83],"algebras.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}
