{"id":"https://openalex.org/W4409214109","doi":"https://doi.org/10.3390/axioms14040277","title":"Universal Covering System and Borsuk\u2019s Problem in Finite Dimensional Banach Spaces","display_name":"Universal Covering System and Borsuk\u2019s Problem in Finite Dimensional Banach Spaces","publication_year":2025,"publication_date":"2025-04-06","ids":{"openalex":"https://openalex.org/W4409214109","doi":"https://doi.org/10.3390/axioms14040277"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14040277","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040277","pdf_url":null,"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://doi.org/10.3390/axioms14040277","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088558075","display_name":"Xiaoliang Qi","orcid":"https://orcid.org/0000-0002-2480-7242"},"institutions":[{"id":"https://openalex.org/I135714990","display_name":"North University of China","ror":"https://ror.org/047bp1713","country_code":"CN","type":"education","lineage":["https://openalex.org/I135714990"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xincong Qi","raw_affiliation_strings":["School of Mathematics, North University of China, Taiyuan 030051, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, North University of China, Taiyuan 030051, China","institution_ids":["https://openalex.org/I135714990"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059257305","display_name":"Xinling Zhang","orcid":"https://orcid.org/0000-0003-3335-9223"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinling Zhang","raw_affiliation_strings":["School of Mathematics, Harbin Institute of Technology, Harbin 150001, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Harbin Institute of Technology, Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116190784","display_name":"Yunfang Lyu","orcid":"https://orcid.org/0009-0007-1809-1448"},"institutions":[{"id":"https://openalex.org/I100188998","display_name":"Harbin University of Science and Technology","ror":"https://ror.org/04e6y1282","country_code":"CN","type":"education","lineage":["https://openalex.org/I100188998"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunfang Lyu","raw_affiliation_strings":["Department of Applied Mathematics, Harbin University of Science and Technology, Harbin 150080, China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Harbin University of Science and Technology, Harbin 150080, China","institution_ids":["https://openalex.org/I100188998"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091557548","display_name":"Senlin Wu","orcid":"https://orcid.org/0000-0003-2499-2836"},"institutions":[{"id":"https://openalex.org/I135714990","display_name":"North University of China","ror":"https://ror.org/047bp1713","country_code":"CN","type":"education","lineage":["https://openalex.org/I135714990"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Senlin Wu","raw_affiliation_strings":["School of Mathematics, North University of China, Taiyuan 030051, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, North University of China, Taiyuan 030051, China","institution_ids":["https://openalex.org/I135714990"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5088558075"],"corresponding_institution_ids":["https://openalex.org/I135714990"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":4.0393,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.89438045,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"14","issue":"4","first_page":"277","last_page":"277"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13234","display_name":"advanced mathematical theories","score":0.9395999908447266,"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/T13234","display_name":"advanced mathematical theories","score":0.9395999908447266,"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":0.923799991607666,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9067999720573425,"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/banach-space","display_name":"Banach space","score":0.679966151714325},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5695840120315552},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38689330220222473},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3600063920021057}],"concepts":[{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.679966151714325},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5695840120315552},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38689330220222473},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3600063920021057}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14040277","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040277","pdf_url":null,"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:6115c762c5694dd38bb2c180fed0f1ce","is_oa":true,"landing_page_url":"https://doaj.org/article/6115c762c5694dd38bb2c180fed0f1ce","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 14, Iss 4, p 277 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14040277","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040277","pdf_url":null,"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":[{"id":"https://openalex.org/G3581671365","display_name":null,"funder_award_id":"12201581","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6844728755","display_name":null,"funder_award_id":"12071444","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W934230699","https://openalex.org/W1540748742","https://openalex.org/W1807179603","https://openalex.org/W1969331458","https://openalex.org/W1977021082","https://openalex.org/W2012513642","https://openalex.org/W2035336359","https://openalex.org/W2053921020","https://openalex.org/W2073482379","https://openalex.org/W2094160323","https://openalex.org/W2106471982","https://openalex.org/W3163684317","https://openalex.org/W3183651628","https://openalex.org/W4283069053","https://openalex.org/W4313309344","https://openalex.org/W4366829281","https://openalex.org/W4376139185","https://openalex.org/W4386484771","https://openalex.org/W4391930804","https://openalex.org/W4392750608","https://openalex.org/W4400878071","https://openalex.org/W4409214109","https://openalex.org/W6640175749"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"For":[0],"each":[1,8,21],"n-dimensional":[2],"real":[3],"Banach":[4],"space":[5],"X":[6,54],"and":[7,55,76,94],"positive":[9],"integer":[10],"m,":[11],"let":[12],"\u03b2(X,m)":[13,49,73],"be":[14,28],"the":[15,31,61,64],"infimum":[16],"of":[17,33,36,48,53,63,104],"\u03b4\u2208(0,1]":[18],"such":[19],"that":[20,98],"set":[22],"A\u2286X":[23],"having":[24],"diameter":[25],"1":[26],"can":[27],"represented":[29],"as":[30],"union":[32],"m":[34,56],"subsets":[35],"A,":[37],"whose":[38],"diameters":[39],"are":[40],"not":[41],"greater":[42],"than":[43],"\u03b4.":[44],"Providing":[45],"accurate":[46],"estimations":[47],"for":[50,59,71],"specific":[51],"choices":[52],"is":[57,81,90,96],"crucial":[58],"addressing":[60],"extension":[62],"classical":[65],"Borsuk\u2019s":[66],"problem.":[67],"A":[68],"general":[69],"framework":[70],"estimating":[72],"via":[74],"constructing":[75],"refining":[77],"universal":[78,87,108],"covering":[79,88,109],"systems":[80],"presented.":[82],"As":[83],"an":[84],"example,":[85],"a":[86,101],"system":[89],"constructed":[91],"in":[92,106],"\u211313":[93],"it":[95],"shown":[97],"\u03b2(\u211313,8)\u226411/12":[99],"by":[100],"feasible":[102],"partitioning":[103],"members":[105],"this":[107],"system.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-02-27T16:54:17.756197","created_date":"2025-10-10T00:00:00"}
