{"id":"https://openalex.org/W7122530580","doi":"https://doi.org/10.3390/axioms15010053","title":"Upper Semicontinuous Representations of Semiorders as Interval Orders","display_name":"Upper Semicontinuous Representations of Semiorders as Interval Orders","publication_year":2026,"publication_date":"2026-01-10","ids":{"openalex":"https://openalex.org/W7122530580","doi":"https://doi.org/10.3390/axioms15010053"},"language":"en","primary_location":{"id":"doi:10.3390/axioms15010053","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15010053","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/axioms15010053","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057342805","display_name":"Gianni Bosi","orcid":"https://orcid.org/0000-0002-3799-4630"},"institutions":[{"id":"https://openalex.org/I142444530","display_name":"University of Trieste","ror":"https://ror.org/02n742c10","country_code":"IT","type":"education","lineage":["https://openalex.org/I142444530"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Gianni Bosi","raw_affiliation_strings":["Department of Economics, Business, Mathematics and Statistics, University of Trieste, Via Valerio 4/1, 34127 Trieste, Italy"],"raw_orcid":"https://orcid.org/0000-0002-3799-4630","affiliations":[{"raw_affiliation_string":"Department of Economics, Business, Mathematics and Statistics, University of Trieste, Via Valerio 4/1, 34127 Trieste, Italy","institution_ids":["https://openalex.org/I142444530"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122810960","display_name":"Gabriele Sbaiz","orcid":null},"institutions":[{"id":"https://openalex.org/I142444530","display_name":"University of Trieste","ror":"https://ror.org/02n742c10","country_code":"IT","type":"education","lineage":["https://openalex.org/I142444530"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gabriele Sbaiz","raw_affiliation_strings":["Department of Economics, Business, Mathematics and Statistics, University of Trieste, Via Valerio 4/1, 34127 Trieste, Italy"],"raw_orcid":"https://orcid.org/0000-0003-3500-6843","affiliations":[{"raw_affiliation_string":"Department of Economics, Business, Mathematics and Statistics, University of Trieste, Via Valerio 4/1, 34127 Trieste, Italy","institution_ids":["https://openalex.org/I142444530"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018665040","display_name":"Magal\u00ec Zuanon","orcid":"https://orcid.org/0000-0001-9311-6325"},"institutions":[{"id":"https://openalex.org/I79940851","display_name":"University of Brescia","ror":"https://ror.org/02q2d2610","country_code":"IT","type":"education","lineage":["https://openalex.org/I79940851"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Magal\u00ec Zuanon","raw_affiliation_strings":["Department of Economics and Management, University of Brescia, Contrada Santa Chiara 50, 25122 Brescia, Italy"],"raw_orcid":"https://orcid.org/0000-0001-9311-6325","affiliations":[{"raw_affiliation_string":"Department of Economics and Management, University of Brescia, Contrada Santa Chiara 50, 25122 Brescia, Italy","institution_ids":["https://openalex.org/I79940851"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057342805"],"corresponding_institution_ids":["https://openalex.org/I142444530"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08577833,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"1","first_page":"53","last_page":"53"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.2215999960899353,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.2215999960899353,"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":0.2054000049829483,"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/T12137","display_name":"Economic theories and models","score":0.15780000388622284,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.769599974155426},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6696000099182129},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5501000285148621},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.4968999922275543},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4147999882698059},{"id":"https://openalex.org/keywords/second-countable-space","display_name":"Second-countable space","score":0.40049999952316284},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.3986000120639801},{"id":"https://openalex.org/keywords/maximal-element","display_name":"Maximal element","score":0.38429999351501465}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8956000208854675},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.769599974155426},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6696000099182129},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5501000285148621},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.4968999922275543},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42640000581741333},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4147999882698059},{"id":"https://openalex.org/C162362422","wikidata":"https://www.wikidata.org/wiki/Q1363919","display_name":"Second-countable space","level":3,"score":0.40049999952316284},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3986000120639801},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3946000039577484},{"id":"https://openalex.org/C196773441","wikidata":"https://www.wikidata.org/wiki/Q1475294","display_name":"Maximal element","level":3,"score":0.38429999351501465},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.36660000681877136},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35839998722076416},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.35420000553131104},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3346000015735626},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3239000141620636},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms15010053","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15010053","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:arts.units.it:11368/3123518","is_oa":false,"landing_page_url":"https://hdl.handle.net/11368/3123518","pdf_url":null,"source":{"id":"https://openalex.org/S4306400480","display_name":"ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142444530","host_organization_name":"University of Trieste","host_organization_lineage":["https://openalex.org/I142444530"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:23fd717e85dd4fe08517bec65c62d380","is_oa":true,"landing_page_url":"https://doaj.org/article/23fd717e85dd4fe08517bec65c62d380","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":"Axioms, Vol 15, Iss 1, p 53 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms15010053","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15010053","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":[{"display_name":"Reduced inequalities","score":0.5362932085990906,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,81],"characterize":[1,83],"the":[2,38,46,53,59,84,102],"upper":[3,20,60,71,79,89],"semicontinuous":[4,21,61,90],"representability":[5],"of":[6,19,32,37,87,104],"a":[7,16,25,29,42,56,69,75,99],"semiorder":[8],"\u227a":[9],"as":[10],"an":[11,88],"interval":[12],"order":[13,49],"(namely,":[14],"by":[15],"pair":[17],"(u,v)":[18],"real-valued":[22],"functions)":[23],"on":[24,107],"topological":[26],"space":[27],"with":[28,52,98],"countable":[30],"basis":[31],"open":[33],"sets,":[34],"where":[35],"one":[36],"representing":[39],"functions":[40],"is":[41],"one-way":[43,91],"utility":[44,92],"for":[45,93],"characteristic":[47,95],"weak":[48,96],"\u227a0":[50],"associated":[51],"semiorder.":[54],"Such":[55],"description":[57],"generalizes":[58],"threshold":[62],"representation.":[63],"To":[64],"this":[65,94],"end,":[66],"we":[67],"introduce":[68],"suitable":[70],"semicontinuity":[72],"condition":[73],"concerning":[74],"semiorder,":[76],"namely":[77],"strict":[78],"semicontinuity.":[80],"further":[82],"mere":[85],"existence":[86],"order,":[97],"view":[100],"to":[101],"identification":[103],"maximal":[105],"elements":[106],"compact":[108],"metric":[109],"spaces.":[110]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2026-01-13T00:00:00"}
