{"id":"https://openalex.org/W2571030091","doi":"https://doi.org/10.23638/lmcs-13(3:12)2017","title":"A Note on the Topologicity of Quantale-Valued Topological Spaces","display_name":"A Note on the Topologicity of Quantale-Valued Topological Spaces","publication_year":2017,"publication_date":"2017-08-15","ids":{"openalex":"https://openalex.org/W2571030091","doi":"https://doi.org/10.23638/lmcs-13(3:12)2017","mag":"2571030091"},"language":"en","primary_location":{"id":"doi:10.23638/lmcs-13(3:12)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(3:12)2017","pdf_url":null,"source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.23638/lmcs-13(3:12)2017","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080074985","display_name":"Hongliang Lai","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hongliang Lai","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5024663910","display_name":"Walter Tholen","orcid":"https://orcid.org/0000-0003-2167-9449"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Walter Tholen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080074985"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5388,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70153807,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"Volume 13, Issue 3","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9990000128746033,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9919000267982483,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7954590916633606},{"id":"https://openalex.org/keywords/monad","display_name":"Monad (category theory)","score":0.7352104187011719},{"id":"https://openalex.org/keywords/distributivity","display_name":"Distributivity","score":0.6977052688598633},{"id":"https://openalex.org/keywords/ultrafilter","display_name":"Ultrafilter","score":0.6873010993003845},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.6319674253463745},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5861448645591736},{"id":"https://openalex.org/keywords/subcategory","display_name":"Subcategory","score":0.5705615282058716},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.5021045207977295},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.4927690327167511},{"id":"https://openalex.org/keywords/category-of-topological-spaces","display_name":"Category of topological spaces","score":0.47979146242141724},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4670718312263489},{"id":"https://openalex.org/keywords/joins","display_name":"Joins","score":0.4606130123138428},{"id":"https://openalex.org/keywords/closed-set","display_name":"Closed set","score":0.44765719771385193},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.438925176858902},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.43638747930526733},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3512832522392273},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34200388193130493},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.2374296486377716},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.14265617728233337},{"id":"https://openalex.org/keywords/topological-tensor-product","display_name":"Topological tensor product","score":0.12416267395019531},{"id":"https://openalex.org/keywords/functional-analysis","display_name":"Functional analysis","score":0.11361154913902283},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09642383456230164},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08141025900840759}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7954590916633606},{"id":"https://openalex.org/C33959348","wikidata":"https://www.wikidata.org/wiki/Q1630568","display_name":"Monad (category theory)","level":3,"score":0.7352104187011719},{"id":"https://openalex.org/C138390121","wikidata":"https://www.wikidata.org/wiki/Q5283219","display_name":"Distributivity","level":3,"score":0.6977052688598633},{"id":"https://openalex.org/C87598191","wikidata":"https://www.wikidata.org/wiki/Q1571831","display_name":"Ultrafilter","level":2,"score":0.6873010993003845},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.6319674253463745},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5861448645591736},{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.5705615282058716},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.5021045207977295},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.4927690327167511},{"id":"https://openalex.org/C83177873","wikidata":"https://www.wikidata.org/wiki/Q2000555","display_name":"Category of topological spaces","level":5,"score":0.47979146242141724},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4670718312263489},{"id":"https://openalex.org/C2778692605","wikidata":"https://www.wikidata.org/wiki/Q4041866","display_name":"Joins","level":2,"score":0.4606130123138428},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.44765719771385193},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.438925176858902},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.43638747930526733},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3512832522392273},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34200388193130493},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2374296486377716},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.14265617728233337},{"id":"https://openalex.org/C178099376","wikidata":"https://www.wikidata.org/wiki/Q7825044","display_name":"Topological tensor product","level":4,"score":0.12416267395019531},{"id":"https://openalex.org/C55112680","wikidata":"https://www.wikidata.org/wiki/Q190549","display_name":"Functional analysis","level":3,"score":0.11361154913902283},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09642383456230164},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08141025900840759},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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":3,"locations":[{"id":"doi:10.23638/lmcs-13(3:12)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(3:12)2017","pdf_url":null,"source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1612.09504","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.09504","pdf_url":"https://arxiv.org/pdf/1612.09504","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.1612.09504","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1612.09504","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.23638/lmcs-13(3:12)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(3:12)2017","pdf_url":null,"source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W629721292","https://openalex.org/W646382222","https://openalex.org/W1525647423","https://openalex.org/W1534787852","https://openalex.org/W1558267995","https://openalex.org/W1607143201","https://openalex.org/W1878777770","https://openalex.org/W1987556478","https://openalex.org/W2035060913","https://openalex.org/W2055390537","https://openalex.org/W2063428732","https://openalex.org/W2083870361","https://openalex.org/W2095257592","https://openalex.org/W2107352447","https://openalex.org/W2113102888","https://openalex.org/W2129008598","https://openalex.org/W2339098090","https://openalex.org/W2565387547","https://openalex.org/W2578456536"],"related_works":["https://openalex.org/W2146563885","https://openalex.org/W4297686489","https://openalex.org/W4226198558","https://openalex.org/W1970567418","https://openalex.org/W1968990996","https://openalex.org/W3213139402","https://openalex.org/W3098518392","https://openalex.org/W2057843304","https://openalex.org/W57183862","https://openalex.org/W4301255297"],"abstract_inverted_index":{"For":[0],"a":[1,17,44,71,82,90,107,114,128,134],"quantale":[2],"${\\sf{V}}$,":[3],"the":[4,40,48,75,121,145,151,155],"category":[5,92,116],"$\\sf":[6],"V$-${\\bf":[7],"Top}$":[8],"of":[9,20,33,36,43,47,55,74,142,157],"${\\sf{V}}$-valued":[10,22,79],"topological":[11,37,91,115],"spaces":[12,24,38,62],"may":[13],"be":[14,68,89,127],"introduced":[15],"as":[16,39],"full":[18],"subcategory":[19],"those":[21],"closure":[23,26],"whose":[25],"operation":[27],"preserves":[28],"finite":[29],"joins.":[30],"In":[31,102],"generalization":[32],"Barr's":[34],"characterization":[35],"lax":[41,45,72],"algebras":[42],"extension":[46,73],"ultrafilter":[49,76],"monad":[50,77],"from":[51],"maps":[52],"to":[53,67,78,88],"relations":[54],"sets,":[56],"for":[57],"${\\sf{V}}$":[58,98,126,132,143],"completely":[59,100],"distributive,":[60],"${\\sf{V}}$-topological":[61],"have":[63],"recently":[64],"been":[65],"shown":[66],"characterizable":[69],"by":[70],"relations.":[80],"As":[81],"consequence,":[83],"${\\sf{V}}$-$\\bf":[84,111],"Top$":[85,112],"is":[86,99,113,133,159],"seen":[87],"over":[93,117],"$\\bf":[94,118],"Set$,":[95],"provided":[96],"that":[97,110,125,137],"distributive.":[101],"this":[103],"paper":[104],"we":[105],"give":[106],"choice-free":[108],"proof":[109],"Set$":[119],"under":[120],"considerably":[122],"milder":[123],"provision":[124,138],"spatial":[129],"coframe.":[130],"When":[131],"continuous":[135],"lattice,":[136],"yields":[139],"complete":[140],"distributivity":[141],"in":[144,150],"constructive":[146],"sense,":[147],"hence":[148],"also":[149],"ordinary":[152],"sense":[153],"whenever":[154],"Axiom":[156],"Choice":[158],"granted.":[160]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}