{"id":"https://openalex.org/W3157686012","doi":"https://doi.org/10.2478/forma-2020-0020","title":"A Case Study of Transporting Urysohn\u2019s Lemma from Topology via Open Sets into Topology via Neighborhoods","display_name":"A Case Study of Transporting Urysohn\u2019s Lemma from Topology via Open Sets into Topology via Neighborhoods","publication_year":2020,"publication_date":"2020-10-01","ids":{"openalex":"https://openalex.org/W3157686012","doi":"https://doi.org/10.2478/forma-2020-0020","mag":"3157686012"},"language":"en","primary_location":{"id":"doi:10.2478/forma-2020-0020","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2020-0020","pdf_url":null,"source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.2478/forma-2020-0020","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068514239","display_name":"Roland Coghetto","orcid":"https://orcid.org/0000-0002-4901-0766"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Roland Coghetto","raw_affiliation_strings":["Rue de la Brasserie 5 , La Louvi\u00e8re , , Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rue de la Brasserie 5 , La Louvi\u00e8re , , Belgium","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5068514239"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23400948,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"3","first_page":"227","last_page":"237"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9969000220298767,"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":0.9969000220298767,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9907000064849854,"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/T10142","display_name":"Formal Methods in Verification","score":0.9645000100135803,"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/hol","display_name":"HOL","score":0.7161984443664551},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.6655351519584656},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5890086889266968},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5559164881706238},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5526981353759766},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5387687683105469},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5211013555526733},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46666353940963745},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37358900904655457},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32250869274139404},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2089693248271942},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09307718276977539},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.08160719275474548}],"concepts":[{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.7161984443664551},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.6655351519584656},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5890086889266968},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5559164881706238},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5526981353759766},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5387687683105469},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5211013555526733},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46666353940963745},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37358900904655457},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32250869274139404},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2089693248271942},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09307718276977539},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.08160719275474548},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/forma-2020-0020","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2020-0020","pdf_url":null,"source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d12a88db18b74e679484856d32281a7e","is_oa":false,"landing_page_url":"https://doaj.org/article/d12a88db18b74e679484856d32281a7e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 28, Iss 3, Pp 227-237 (2020)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/10841","is_oa":false,"landing_page_url":"http://hdl.handle.net/11320/10841","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"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":"Article"}],"best_oa_location":{"id":"doi:10.2478/forma-2020-0020","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2020-0020","pdf_url":null,"source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.7300000190734863,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W101424827","https://openalex.org/W1020805281","https://openalex.org/W1205312757","https://openalex.org/W1579317989","https://openalex.org/W1649012353","https://openalex.org/W1751036247","https://openalex.org/W2099252149","https://openalex.org/W2129270522","https://openalex.org/W2137109977","https://openalex.org/W2158336522","https://openalex.org/W2295728669","https://openalex.org/W2316140067","https://openalex.org/W2770430340","https://openalex.org/W2886891016","https://openalex.org/W2978296386","https://openalex.org/W3011813664","https://openalex.org/W3012312608","https://openalex.org/W3113233883"],"related_works":["https://openalex.org/W2585743557","https://openalex.org/W1985243371","https://openalex.org/W1581380057","https://openalex.org/W3098927713","https://openalex.org/W1819460135","https://openalex.org/W4295798319","https://openalex.org/W1998171255","https://openalex.org/W4313389715","https://openalex.org/W4221036368","https://openalex.org/W4320085668"],"abstract_inverted_index":{"Summary":[0],"J\u00f3zef":[1],"Bia\u0142as":[2],"and":[3,46,85,115,212,282,288,292,365],"Yatsuka":[4],"Nakamura":[5],"has":[6],"completely":[7],"formalized":[8],"a":[9,22,134,195,218,266,369],"proof":[10],"of":[11,21,89,133,286,290,297,312,341,391],"Urysohn\u2019s":[12,155,353,396],"lemma":[13,156,354,397],"in":[14,18,40,49,217,221,265,275,376,387],"the":[15,19,30,35,50,55,74,80,111,116,123,131,154,222,227,234,295,298,304,328,333,339,352,358,373,388,392],"article":[16,51,81],"[4],":[17],"context":[20],"topological":[23,36,56,106,117,147,330,359],"space":[24,37,57,118,360],"defined":[25,39,59,119,361],"via":[26,60,120,362],"open":[27],"sets.":[28],"In":[29,53,73,161,182,205,226,245,322],"Mizar":[31,95,112,124,150,164,393],"Mathematical":[32],"Library":[33],"(MML),":[34],"is":[38,58,63,108,177,190,249,271],"this":[41,323],"way":[42],"by":[43,338],"Beata":[44],"Padlewska":[45],"Agata":[47],"Darmochwa\u0142":[48],"[18].":[52],"[7]":[54],"neighborhoods.":[61,363],"It":[62,345],"well":[64],"known":[65],"that":[66],"these":[67],"definitions":[68,171,382],"are":[69,262],"equivalent":[70],"[5,":[71],"6].":[72],"definitions,":[75],"an":[76],"abstract":[77],"structure":[78,113,302],"(i.e.":[79],"[17,":[82],"STRUCT":[83],"0]":[84],"its":[86],"descendants,":[87],"all":[88],"them":[90],"directly":[91,385],"or":[92,172,185],"indirectly":[93],"using":[94],"structures":[96],"[3])":[97],"have":[98,214,230,367],"been":[99,215,231],"used":[100,232],"(see":[101],"[10],":[102],"[9]).":[103],"The":[104,381],"first":[105,325],"definition":[107,296],"based":[109],"on":[110],"TopStruct":[114],"neighborhoods":[121],"with":[122,194],"structure:":[125],"FMT":[126,138],"Space":[127],"Str.":[128],"To":[129],"emphasize":[130],"notion":[132],"neighborhood,":[135],"we":[136,152,326,335],"rename":[137],"TopSpace":[139,158],"(topology":[140],"from":[141,157,300],"neighbourhoods)":[142],"to":[143,159,251,277,293,303,348,357,371],"NTopSpace":[144],"(a":[145],"neighborhood":[146],"space).":[148],"Using":[149],"[2],":[151],"transport":[153,189,294,349],"NTop-Space.":[160],"some":[162,246],"cases,":[163],"allows":[165,346],"certain":[166],"techniques":[167],"for":[168,273],"transporting":[169],"proofs,":[170,247],"theorems.":[173],"Generally":[174],"speaking,":[175],"there":[176],"no":[178],"such":[179],"automatic":[180],"translating.":[181],"Coq,":[183],"Isabelle/HOL":[184,211],"homotopy":[186],"type":[187],"theory":[188],"also":[191],"studied,":[192],"sometimes":[193],"more":[196,350],"systematic":[197],"aim":[198],"[14],":[199],"[21],":[200],"[11],":[201],"[12],":[202],"[8],":[203],"[19].":[204],"[1],":[206],"two":[207,279],"co-existing":[208],"Isabelle":[209,223],"libraries:":[210],"Isabelle/Mizar,":[213],"aligned":[216],"single":[219],"foundation":[220],"logical":[224],"framework.":[225],"MML,":[228],"they":[229],"since":[233],"beginning:":[235],"reconsider,":[236],"registration,":[237],"cluster,":[238],"others":[239],"were":[240,336],"later":[241],"implemented":[242],"[13]:":[243],"identify.":[244],"it":[248],"possible":[250],"define":[252,278],"particular":[253],"functors":[254,280],"between":[255,284],"different":[256],"structures,":[257],"mainly":[258],"useful":[259],"when":[260],"results":[261],"already":[263],"obtained":[264],"given":[267],"structure.":[268],"This":[269],"technique":[270],"used,":[272],"example,":[274],"[15]":[276],"MXR2MXF":[281],"MXF2MXF":[283],"Matrix":[285,289,311],"REAL":[287,313],"F-Real":[291],"addition":[299],"one":[301],"other:":[305],"[...]":[306],"A":[307],"+":[308,318],"B":[309],"-&gt;":[310],"equals":[314],"MXF2MXR":[315],"((MXR2MXF":[316],"A)":[317],"(MXR2MXF":[319],"B))":[320],"[...].":[321],"paper,":[324],"align":[327],"necessary":[329],"concepts.":[331],"For":[332],"formalization,":[334],"inspired":[337],"works":[340],"Claude":[342],"Wagschal":[343],"[20].":[344],"us":[347],"naturally":[351],"([4,":[355],"URYSOHN3:20])":[356],"Nakasho":[364],"Shidama":[366],"developed":[368],"solution":[370],"explore":[372],"notions":[374],"introduced":[375],"various":[377],"ways":[378],"https://mimosa-project.github.io/mmlreference/current/":[379],"[16].":[380],"can":[383],"be":[384],"linked":[386],"HTML":[389],"version":[390],"library":[394],"(example:":[395],"http://mizar.org/version/current/html/urysohn3.html#T20":[398],").":[399]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2021-05-10T00:00:00"}
