{"id":"https://openalex.org/W4282915362","doi":"https://doi.org/10.3390/axioms11060290","title":"Some Cardinal and Geometric Properties of the Space of Permutation Degree","display_name":"Some Cardinal and Geometric Properties of the Space of Permutation Degree","publication_year":2022,"publication_date":"2022-06-14","ids":{"openalex":"https://openalex.org/W4282915362","doi":"https://doi.org/10.3390/axioms11060290"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11060290","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11060290","pdf_url":"https://www.mdpi.com/2075-1680/11/6/290/pdf?version=1655436050","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/6/290/pdf?version=1655436050","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073115325","display_name":"Ljubi\u0161a D. R. Ko\u010dinac","orcid":"https://orcid.org/0000-0002-4870-7908"},"institutions":[{"id":"https://openalex.org/I152518017","display_name":"University of Nis","ror":"https://ror.org/00965bg92","country_code":"RS","type":"education","lineage":["https://openalex.org/I152518017"]}],"countries":["RS"],"is_corresponding":true,"raw_author_name":"Ljubi\u0161a D. R. Ko\u010dinac","raw_affiliation_strings":["Faculty of Sciences and Mathematics, University of Ni\u0161, 18000 Ni\u0161, Serbia"],"affiliations":[{"raw_affiliation_string":"Faculty of Sciences and Mathematics, University of Ni\u0161, 18000 Ni\u0161, Serbia","institution_ids":["https://openalex.org/I152518017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019029292","display_name":"F. G. Mukhamadiev","orcid":"https://orcid.org/0000-0002-1892-4899"},"institutions":[{"id":"https://openalex.org/I47151758","display_name":"National University of Uzbekistan","ror":"https://ror.org/011647w73","country_code":"UZ","type":"education","lineage":["https://openalex.org/I47151758"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Farkhod G. Mukhamadiev","raw_affiliation_strings":["Department of Mathematics, National University of Uzbekistan named after Mirzo Ulugbek, Str. University 4, Tashkent 100174, Uzbekistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National University of Uzbekistan named after Mirzo Ulugbek, Str. University 4, Tashkent 100174, Uzbekistan","institution_ids":["https://openalex.org/I47151758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054631533","display_name":"Anvar K. Sadullaev","orcid":"https://orcid.org/0000-0002-4373-2792"},"institutions":[{"id":"https://openalex.org/I4210149746","display_name":"Kimyo International University in Tashkent","ror":"https://ror.org/05jfh7098","country_code":"UZ","type":"facility","lineage":["https://openalex.org/I4210149746"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Anvar K. Sadullaev","raw_affiliation_strings":["Yeoju Technical Institute in Tashkent, Str. Usman Nasyr 156, Tashkent 100121, Uzbekistan"],"affiliations":[{"raw_affiliation_string":"Yeoju Technical Institute in Tashkent, Str. Usman Nasyr 156, Tashkent 100121, Uzbekistan","institution_ids":["https://openalex.org/I4210149746"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073115325"],"corresponding_institution_ids":["https://openalex.org/I152518017"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":4.7041,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.96237767,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"11","issue":"6","first_page":"290","last_page":"290"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9991000294685364,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9696000218391418,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9520000219345093,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8394113183021545},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.7603685855865479},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.6638851761817932},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6089749336242676},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5713441371917725},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5119761228561401},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.49584731459617615},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.44849538803100586},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3615034222602844},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0748225748538971}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8394113183021545},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.7603685855865479},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.6638851761817932},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6089749336242676},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5713441371917725},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5119761228561401},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.49584731459617615},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.44849538803100586},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3615034222602844},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0748225748538971},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11060290","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11060290","pdf_url":"https://www.mdpi.com/2075-1680/11/6/290/pdf?version=1655436050","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f5661648756a4247b085c5cfc469571f","is_oa":true,"landing_page_url":"https://doaj.org/article/f5661648756a4247b085c5cfc469571f","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 6, p 290 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/6/290/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11060290","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":"Axioms; Volume 11; Issue 6; Pages: 290","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11060290","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11060290","pdf_url":"https://www.mdpi.com/2075-1680/11/6/290/pdf?version=1655436050","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4282915362.pdf","grobid_xml":"https://content.openalex.org/works/W4282915362.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W177012147","https://openalex.org/W622048345","https://openalex.org/W1505249882","https://openalex.org/W1966292717","https://openalex.org/W1968716310","https://openalex.org/W2027614607","https://openalex.org/W2114395398","https://openalex.org/W2131044967","https://openalex.org/W2241332607","https://openalex.org/W2318333845","https://openalex.org/W3107847882","https://openalex.org/W3115934376","https://openalex.org/W3122492091","https://openalex.org/W6619741997","https://openalex.org/W6630044590","https://openalex.org/W6679188283"],"related_works":["https://openalex.org/W2002177687","https://openalex.org/W2058438338","https://openalex.org/W2997091376","https://openalex.org/W2019471580","https://openalex.org/W3161230432","https://openalex.org/W1615487630","https://openalex.org/W2941284322","https://openalex.org/W95605005","https://openalex.org/W4293316580","https://openalex.org/W2168299207"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,41,46,62,112],"devoted":[3],"to":[4],"the":[5,12,25,28,31,38,49,65,69,72,83,92,109],"investigation":[6],"of":[7,30,34,37,57,74],"cardinal":[8],"invariants":[9],"such":[10],"as":[11],"hereditary":[13,15,19],"density,":[14,17],"weak":[16],"and":[18,27,71,86,95],"Lindel\u00f6f":[20],"number.":[21],"The":[22],"relation":[23],"between":[24],"spread":[26],"extent":[29],"space":[32,40,50],"SP2(R,\u03c4(A))":[33],"permutation":[35],"degree":[36],"Hattori":[39],"discussed.":[42],"In":[43,77],"particular,":[44],"it":[45,61,104],"shown":[47,63],"that":[48,64,81,108],"SP2(R,\u03c4S)":[51],"contains":[52],"a":[53,102,113],"closed":[54],"discrete":[55],"subset":[56],"cardinality":[58],"c.":[59],"Moreover,":[60],"functor":[66,110],"SPGn":[67,111],"preserves":[68],"homotopy":[70,115],"retraction":[73],"topological":[75],"spaces.":[76],"addition,":[78],"we":[79],"prove":[80],"if":[82],"spaces":[84,93],"X":[85],"Y":[87],"are":[88,97],"homotopically":[89,99],"equivalent,":[90],"then":[91],"SPGnX":[94],"SPGnY":[96],"also":[98],"equivalent.":[100],"As":[101],"result,":[103],"has":[105],"been":[106],"proved":[107],"covariant":[114],"functor.":[116]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-06-16T00:00:00"}