{"id":"https://openalex.org/W3089005368","doi":"https://doi.org/10.3390/sym12091557","title":"On Product of Smooth Neutrosophic Topological Spaces","display_name":"On Product of Smooth Neutrosophic Topological Spaces","publication_year":2020,"publication_date":"2020-09-21","ids":{"openalex":"https://openalex.org/W3089005368","doi":"https://doi.org/10.3390/sym12091557","mag":"3089005368"},"language":"en","primary_location":{"id":"doi:10.3390/sym12091557","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12091557","pdf_url":"https://www.mdpi.com/2073-8994/12/9/1557/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/9/1557/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040985677","display_name":"Kalaivani Chandran","orcid":"https://orcid.org/0000-0003-3632-2282"},"institutions":[{"id":"https://openalex.org/I916357946","display_name":"Sri Sivasubramaniya Nadar College of Engineering","ror":"https://ror.org/054psm803","country_code":"IN","type":"education","lineage":["https://openalex.org/I916357946"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Kalaivani Chandran","raw_affiliation_strings":["Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam 603110, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam 603110, India","institution_ids":["https://openalex.org/I916357946"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005336660","display_name":"Swathi Sundari Sundaramoorthy","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Swathi Sundari Sundaramoorthy","raw_affiliation_strings":["Department of Mathematics, V. V. Vanniaperumal College for Women, Virudhunagar 626001, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, V. V. Vanniaperumal College for Women, Virudhunagar 626001, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012703845","display_name":"Florent\u00edn Smarandache","orcid":"https://orcid.org/0000-0002-5560-5926"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]},{"id":"https://openalex.org/I4210118010","display_name":"Gallup Indian Medical Center","ror":"https://ror.org/02jbzrw51","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I1299022934","https://openalex.org/I157850169","https://openalex.org/I4210118010"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Florentin Smarandache","raw_affiliation_strings":["Department of Mathematics and Science, University of New Mexico, Gallup, NM 87301, USA"],"raw_orcid":"https://orcid.org/0000-0002-5560-5926","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Science, University of New Mexico, Gallup, NM 87301, USA","institution_ids":["https://openalex.org/I169521973","https://openalex.org/I4210118010"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107657642","display_name":"Saeid Jafari","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saeid Jafari","raw_affiliation_strings":["Department of Mathematics, College of Vestsjaelland South, Herrestrade 11, 4200 Slagelse, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Vestsjaelland South, Herrestrade 11, 4200 Slagelse, Denmark","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040985677"],"corresponding_institution_ids":["https://openalex.org/I916357946"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.14188752,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"12","issue":"9","first_page":"1557","last_page":"1557"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9991999864578247,"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":0.9991999864578247,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9940999746322632,"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":0.9786999821662903,"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/product-topology","display_name":"Product topology","score":0.7384370565414429},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.6553021669387817},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.6233096718788147},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.6147791743278503},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5863195657730103},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5578116774559021},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5323655605316162},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48752424120903015},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4488633871078491},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33429181575775146},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.17019057273864746},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10772815346717834},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.051370829343795776}],"concepts":[{"id":"https://openalex.org/C123222754","wikidata":"https://www.wikidata.org/wiki/Q1070472","display_name":"Product topology","level":2,"score":0.7384370565414429},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.6553021669387817},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.6233096718788147},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.6147791743278503},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5863195657730103},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5578116774559021},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5323655605316162},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48752424120903015},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4488633871078491},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33429181575775146},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.17019057273864746},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10772815346717834},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.051370829343795776},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym12091557","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12091557","pdf_url":"https://www.mdpi.com/2073-8994/12/9/1557/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:digitalrepository.unm.edu:math_fsp-1495","is_oa":true,"landing_page_url":"https://digitalrepository.unm.edu/math_fsp/455","pdf_url":null,"source":{"id":"https://openalex.org/S4377196368","display_name":"UNM\u2019s Digital Repository (University of New Mexico)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169521973","host_organization_name":"University of New Mexico","host_organization_lineage":["https://openalex.org/I169521973"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics and Statistics Faculty and Staff Publications","raw_type":null},{"id":"pmh:oai:doaj.org/article:73c22f81ee2c44489dae731d029c0fb9","is_oa":true,"landing_page_url":"https://doaj.org/article/73c22f81ee2c44489dae731d029c0fb9","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 9, p 1557 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/9/1557/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12091557","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12091557","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12091557","pdf_url":"https://www.mdpi.com/2073-8994/12/9/1557/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.5199999809265137}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W58991120","https://openalex.org/W2002541167","https://openalex.org/W2016180799","https://openalex.org/W2057010687","https://openalex.org/W2186737070","https://openalex.org/W2235799607","https://openalex.org/W2362779022","https://openalex.org/W2371332014","https://openalex.org/W2478219847","https://openalex.org/W2794107195","https://openalex.org/W2962693862","https://openalex.org/W2970284467","https://openalex.org/W3001377282","https://openalex.org/W3045281011","https://openalex.org/W3093143365","https://openalex.org/W3119615233","https://openalex.org/W4247655907","https://openalex.org/W6602379895","https://openalex.org/W6737074971"],"related_works":["https://openalex.org/W437370296","https://openalex.org/W2379886056","https://openalex.org/W4301315464","https://openalex.org/W4301479830","https://openalex.org/W2515833534","https://openalex.org/W2073102211","https://openalex.org/W2963837678","https://openalex.org/W2521640161","https://openalex.org/W2941717049","https://openalex.org/W2376559523"],"abstract_inverted_index":{"In":[0],"this":[1,62],"paper,":[2],"we":[3,23,52],"develop":[4],"the":[5,8,25,41,46,56,65],"notion":[6,26],"of":[7,27,48,58,67],"basis":[9],"for":[10],"a":[11,16,21],"smooth":[12],"neutrosophic":[13,29],"topology":[14],"in":[15,61],"more":[17],"natural":[18],"way.":[19],"As":[20],"sequel,":[22],"define":[24,53],"symmetric":[28],"quasi-coincident":[30],"neighborhood":[31],"systems":[32],"and":[33,54],"prove":[34],"some":[35],"interesting":[36],"results":[37],"that":[38],"fit":[39],"with":[40],"classical":[42],"ones,":[43],"to":[44],"establish":[45],"consistency":[47],"theory":[49],"developed.":[50],"Finally,":[51],"discuss":[55],"concept":[57],"product":[59],"topology,":[60],"context,":[63],"using":[64],"definition":[66],"basis.":[68]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2020-10-01T00:00:00"}
