{"id":"https://openalex.org/W7224999840","doi":"https://doi.org/10.56143/ujmcs.v2i2.4/","title":"Some Results on the Minkowski Difference in Topological Vector Spaces","display_name":"Some Results on the Minkowski Difference in Topological Vector Spaces","publication_year":2026,"publication_date":"2026-10-31","ids":{"openalex":"https://openalex.org/W7224999840","doi":"https://doi.org/10.56143/ujmcs.v2i2.4/"},"language":"en","primary_location":{"id":"doi:10.56143/ujmcs.v2i2.4/","doi":"https://doi.org/10.56143/ujmcs.v2i2.4/","is_oa":true,"landing_page_url":"https://doi.org/10.56143/ujmcs.v2i2.4/","pdf_url":"https://ujmcs.tstu.uz/index.php/ujmcs/article/download/76/72","source":{"id":"https://openalex.org/S5407051944","display_name":"UZBEKISTAN JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE","issn_l":"3093-8589","issn":["3093-8589","3093-8619"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Uzbekistan Journal of Mathematics and Computer Science","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://ujmcs.tstu.uz/index.php/ujmcs/article/download/76/72","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039754634","display_name":"Adilbek Atakhanovich Zaitov","orcid":"https://orcid.org/0000-0002-2248-0442","observed_orcids":["https://orcid.org/0000-0002-2248-0442"]},"institutions":[{"id":"https://openalex.org/I4210097274","display_name":"Tashkent Institute of Architecture and Civil Engineering","ror":"https://ror.org/00phht511","country_code":"UZ","type":"education","lineage":["https://openalex.org/I4210097274"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Adilbek Zaitov","raw_affiliation_strings":["Tashkent University of Architecture and Civil Engineering"],"raw_orcid":"https://orcid.org/0000-0002-2248-0442","affiliations":[{"raw_affiliation_string":"Tashkent University of Architecture and Civil Engineering","institution_ids":["https://openalex.org/I4210097274"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012124461","display_name":"Jalolxon Nuritdinov","orcid":"https://orcid.org/0000-0001-8288-832X","observed_orcids":["https://orcid.org/0000-0001-8288-832X"]},"institutions":[{"id":"https://openalex.org/I4405263231","display_name":"Kokand State University","ror":"https://ror.org/0468e4316","country_code":"UZ","type":"education","lineage":["https://openalex.org/I4405263231"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Jalolxon Nuritdinov","raw_affiliation_strings":["Kokand State University"],"raw_orcid":"https://orcid.org/0000-0001-8288-832X","affiliations":[{"raw_affiliation_string":"Kokand State University","institution_ids":["https://openalex.org/I4405263231"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.88098506,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":"2","first_page":"48","last_page":"55"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9829000234603882,"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"}},"topics":[{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9829000234603882,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.006200000178068876,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.003000000026077032,"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/minkowski-difference","display_name":"Minkowski difference","score":0.9869999885559082},{"id":"https://openalex.org/keywords/minkowski-sum","display_name":"Minkowski sum","score":0.9909999966621399},{"id":"https://openalex.org/keywords/topological-vector-spaces","display_name":"topological vector spaces","score":0.9800000190734863},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.699999988079071},{"id":"https://openalex.org/keywords/distributivity","display_name":"distributivity","score":0.9750000238418579},{"id":"https://openalex.org/keywords/density-of-sets","display_name":"density of sets","score":0.8379999995231628},{"id":"https://openalex.org/keywords/compact-convex-sets","display_name":"compact convex sets","score":0.8600000143051147}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7501000165939331},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.7170000076293945},{"id":"https://openalex.org/C79013991","wikidata":"https://www.wikidata.org/wiki/Q1097021","display_name":"Minkowski's theorem","level":3,"score":0.6137999892234802},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49239999055862427},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.4749000072479248},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.4163999855518341},{"id":"https://openalex.org/C47776270","wikidata":"https://www.wikidata.org/wiki/Q1455249","display_name":"Topological vector space","level":3,"score":0.41620001196861267},{"id":"https://openalex.org/C154804608","wikidata":"https://www.wikidata.org/wiki/Q2721559","display_name":"Topological manifold","level":5,"score":0.41429999470710754},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.41280001401901245},{"id":"https://openalex.org/C58228006","wikidata":"https://www.wikidata.org/wiki/Q1572357","display_name":"Locally convex topological vector space","level":3,"score":0.4016999900341034},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3887999951839447},{"id":"https://openalex.org/C10728891","wikidata":"https://www.wikidata.org/wiki/Q584521","display_name":"Homeomorphism (graph theory)","level":2,"score":0.38199999928474426},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C178099376","wikidata":"https://www.wikidata.org/wiki/Q7825044","display_name":"Topological tensor product","level":4,"score":0.3343000113964081},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3109999895095825},{"id":"https://openalex.org/C7451433","wikidata":"https://www.wikidata.org/wiki/Q1265039","display_name":"Solenoidal vector field","level":3,"score":0.29840001463890076},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C527218924","wikidata":"https://www.wikidata.org/wiki/Q964053","display_name":"Topological algebra","level":3,"score":0.29249998927116394},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2913999855518341},{"id":"https://openalex.org/C138390121","wikidata":"https://www.wikidata.org/wiki/Q5283219","display_name":"Distributivity","level":3,"score":0.2856999933719635},{"id":"https://openalex.org/C96386209","wikidata":"https://www.wikidata.org/wiki/Q1046291","display_name":"Topological group","level":3,"score":0.2831000089645386},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2825999855995178},{"id":"https://openalex.org/C180987920","wikidata":"https://www.wikidata.org/wiki/Q922339","display_name":"Topological ring","level":4,"score":0.27810001373291016},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C24977911","wikidata":"https://www.wikidata.org/wiki/Q1491995","display_name":"Connected space","level":3,"score":0.25929999351501465},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.2572000026702881}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.56143/ujmcs.v2i2.4/","doi":"https://doi.org/10.56143/ujmcs.v2i2.4/","is_oa":true,"landing_page_url":"https://doi.org/10.56143/ujmcs.v2i2.4/","pdf_url":"https://ujmcs.tstu.uz/index.php/ujmcs/article/download/76/72","source":{"id":"https://openalex.org/S5407051944","display_name":"UZBEKISTAN JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE","issn_l":"3093-8589","issn":["3093-8589","3093-8619"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Uzbekistan Journal of Mathematics and Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.56143/ujmcs.v2i2.4/","doi":"https://doi.org/10.56143/ujmcs.v2i2.4/","is_oa":true,"landing_page_url":"https://doi.org/10.56143/ujmcs.v2i2.4/","pdf_url":"https://ujmcs.tstu.uz/index.php/ujmcs/article/download/76/72","source":{"id":"https://openalex.org/S5407051944","display_name":"UZBEKISTAN JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE","issn_l":"3093-8589","issn":["3093-8589","3093-8619"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Uzbekistan Journal of Mathematics and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224999840.pdf","grobid_xml":"https://content.openalex.org/works/W7224999840.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W2013475283","https://openalex.org/W2017093751","https://openalex.org/W2941585389","https://openalex.org/W4405904191","https://openalex.org/W4406741481","https://openalex.org/W4409566047","https://openalex.org/W4414482633","https://openalex.org/W7134268407","https://openalex.org/W7140235576"],"related_works":["https://openalex.org/W4414199953","https://openalex.org/W7164492406","https://openalex.org/W245603867","https://openalex.org/W915921549","https://openalex.org/W4392940336","https://openalex.org/W7100158092","https://openalex.org/W2950224501","https://openalex.org/W3122478062","https://openalex.org/W2887592140","https://openalex.org/W4390939286"],"abstract_inverted_index":{"This":[0],"work":[1],"highlights":[2],"important":[3],"topological":[4,11,73],"properties":[5],"of":[6,16,28,38,64],"Minkowski":[7,17,43,56],"operations":[8,21,44],"defined":[9],"in":[10,61],"vector":[12],"spaces.":[13],"The":[14],"distributivity":[15],"sum":[18],"and":[19,68],"difference":[20,57],"with":[22],"respect":[23],"to":[24],"the":[25,35,55,62],"Cartesian":[26],"product":[27],"sets":[29,39],"is":[30,40,49,59,70],"proved.":[31],"Conditions":[32],"under":[33,42],"which":[34],"density":[36],"property":[37],"preserved":[41],"are":[45],"obtained.":[46],"Furthermore,":[47],"it":[48],"established":[50],"as":[51],"a":[52],"theorem":[53],"that":[54],"operation":[58],"continuous":[60],"class":[63],"compact":[65],"convex":[66],"sets,":[67],"this":[69],"proved":[71],"using":[72],"methods.":[74]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-11-01T00:00:00"}