{"id":"https://openalex.org/W4239851161","doi":"https://doi.org/10.1515/forma-2016-0018","title":"Uniform Space","display_name":"Uniform Space","publication_year":2016,"publication_date":"2016-09-01","ids":{"openalex":"https://openalex.org/W4239851161","doi":"https://doi.org/10.1515/forma-2016-0018"},"language":"en","primary_location":{"id":"doi:10.1515/forma-2016-0018","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2016-0018","pdf_url":"https://sciendo.com/pdf/10.1515/forma-2016-0018","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://sciendo.com/pdf/10.1515/forma-2016-0018","any_repository_has_fulltext":true},"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 7100 La Louvi\u00e8re, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rue de la Brasserie 5 7100 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":0.6523,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.77337436,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"24","issue":"3","first_page":"215","last_page":"226"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9973999857902527,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9973999857902527,"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":0.9968000054359436,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9952999949455261,"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/mathematics","display_name":"Mathematics","score":0.7720932960510254},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.6280690431594849},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.5672376751899719},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5450667142868042},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5244760513305664},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.5061149001121521},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.476644366979599},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.46037915349006653},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4567895531654358},{"id":"https://openalex.org/keywords/t1-space","display_name":"T1 space","score":0.44833096861839294},{"id":"https://openalex.org/keywords/zero-dimensional-space","display_name":"Zero-dimensional space","score":0.4371933341026306},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42341870069503784},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37483784556388855},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36311960220336914},{"id":"https://openalex.org/keywords/topological-vector-space","display_name":"Topological vector space","score":0.2613561749458313},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.235047847032547},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1861667037010193},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.07051363587379456}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7720932960510254},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.6280690431594849},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.5672376751899719},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5450667142868042},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5244760513305664},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.5061149001121521},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.476644366979599},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.46037915349006653},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4567895531654358},{"id":"https://openalex.org/C106558176","wikidata":"https://www.wikidata.org/wiki/Q284347","display_name":"T1 space","level":5,"score":0.44833096861839294},{"id":"https://openalex.org/C140936041","wikidata":"https://www.wikidata.org/wiki/Q1801244","display_name":"Zero-dimensional space","level":4,"score":0.4371933341026306},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42341870069503784},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37483784556388855},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36311960220336914},{"id":"https://openalex.org/C47776270","wikidata":"https://www.wikidata.org/wiki/Q1455249","display_name":"Topological vector space","level":3,"score":0.2613561749458313},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.235047847032547},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1861667037010193},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07051363587379456},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1515/forma-2016-0018","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2016-0018","pdf_url":"https://sciendo.com/pdf/10.1515/forma-2016-0018","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:6a8db6d7500a4c52abdb50931f04f9d2","is_oa":false,"landing_page_url":"https://doaj.org/article/6a8db6d7500a4c52abdb50931f04f9d2","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 24, Iss 3, Pp 215-226 (2016)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/5556","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/5556","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1515/forma-2016-0018","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2016-0018","pdf_url":"https://sciendo.com/pdf/10.1515/forma-2016-0018","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":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4239851161.pdf","grobid_xml":"https://content.openalex.org/works/W4239851161.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1861699494","https://openalex.org/W2144731472","https://openalex.org/W2295728669"],"related_works":["https://openalex.org/W2186562938","https://openalex.org/W2383601889","https://openalex.org/W113867295","https://openalex.org/W251914771","https://openalex.org/W4286361356","https://openalex.org/W2048589980","https://openalex.org/W2356702416","https://openalex.org/W1560259765","https://openalex.org/W3194620379","https://openalex.org/W3022742563"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"article,":[3],"we":[4,48,62],"formalize":[5],"in":[6],"Mizar":[7],"[1]":[8],"the":[9,19,37,50,53,57,64,72,95,98],"notion":[10],"of":[11,21,39,43,52,97],"uniform":[12,29,73,91],"space":[13,30,66,74,92],"introduced":[14],"by":[15,68,76],"Andr\u00e9":[16],"Weil":[17],"using":[18,81],"concepts":[20,38],"entourages":[22],"[2].":[23],"We":[24,35],"present":[25],"some":[26],"results":[27],"between":[28],"and":[31,41,71,85],"pseudo":[32],"metric":[33],"space.":[34],"introduce":[36],"left-uniformity":[40],"right-uniformity":[42],"a":[44,69,89],"topological":[45],"group.":[46],"Next,":[47],"define":[49,63],"concept":[51],"partition":[54],"topology.":[55],"Following":[56],"Vlach\u2019s":[58],"works":[59],"[11,":[60],"10],":[61],"semi-uniform":[65],"induced":[67,75],"tolerance":[70],"an":[77],"equivalence":[78],"relation.":[79],"Finally,":[80],"mostly":[82],"Gehrke,":[83],"Grigorieff":[84],"Pin":[86],"[4]":[87],"works,":[88],"Pervin":[90],"defined":[93],"from":[94],"sets":[96],"form":[99],"((X\\A)":[100],"\u00d7":[101],"(X\\A))":[102],"\u222a":[103],"(A\u00d7A)":[104],"is":[105],"presented.":[106]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2022-05-12T00:00:00"}