{"id":"https://openalex.org/W4408090908","doi":"https://doi.org/10.3390/axioms14030188","title":"Net-Compact Hausdorff Topologies and Continuous Multi-Utility Representations for Closed Preorders","display_name":"Net-Compact Hausdorff Topologies and Continuous Multi-Utility Representations for Closed Preorders","publication_year":2025,"publication_date":"2025-03-03","ids":{"openalex":"https://openalex.org/W4408090908","doi":"https://doi.org/10.3390/axioms14030188"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14030188","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14030188","pdf_url":"https://www.mdpi.com/2075-1680/14/3/188/pdf?version=1741006681","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/2075-1680/14/3/188/pdf?version=1741006681","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":["DEAMS, Universit\u00e0 di Trieste, 34127 Trieste, Italy"],"affiliations":[{"raw_affiliation_string":"DEAMS, Universit\u00e0 di Trieste, 34127 Trieste, Italy","institution_ids":["https://openalex.org/I142444530"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090257881","display_name":"Gabriele Sbaiz","orcid":"https://orcid.org/0000-0003-3500-6843"},"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":["DEAMS, Universit\u00e0 di Trieste, 34127 Trieste, Italy"],"affiliations":[{"raw_affiliation_string":"DEAMS, Universit\u00e0 di Trieste, 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":["DEM, Universit\u00e0 di Brescia, 25123 Brescia, Italy"],"affiliations":[{"raw_affiliation_string":"DEM, Universit\u00e0 di Brescia, 25123 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":4.6194,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.8929812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"14","issue":"3","first_page":"188","last_page":"188"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9916999936103821,"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":0.9916999936103821,"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":0.9842000007629395,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9799000024795532,"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/hausdorff-space","display_name":"Hausdorff space","score":0.712952733039856},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.5976826548576355},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5120659470558167},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4863327145576477},{"id":"https://openalex.org/keywords/net","display_name":"Net (polyhedron)","score":0.4822271764278412},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3343873620033264},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32337531447410583},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20395267009735107},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10574996471405029},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.04589381814002991}],"concepts":[{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.712952733039856},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.5976826548576355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5120659470558167},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4863327145576477},{"id":"https://openalex.org/C14166107","wikidata":"https://www.wikidata.org/wiki/Q253829","display_name":"Net (polyhedron)","level":2,"score":0.4822271764278412},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3343873620033264},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32337531447410583},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20395267009735107},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10574996471405029},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.04589381814002991}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms14030188","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14030188","pdf_url":"https://www.mdpi.com/2075-1680/14/3/188/pdf?version=1741006681","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:11368/3106198","is_oa":true,"landing_page_url":"https://hdl.handle.net/11368/3106198","pdf_url":null,"source":{"id":"https://openalex.org/S4306402362","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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:a68855cecb9841abbf789d9e3250b2cc","is_oa":true,"landing_page_url":"https://doaj.org/article/a68855cecb9841abbf789d9e3250b2cc","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 3, p 188 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14030188","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14030188","pdf_url":"https://www.mdpi.com/2075-1680/14/3/188/pdf?version=1741006681","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":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4408090908.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W424802240","https://openalex.org/W1968524630","https://openalex.org/W1979930662","https://openalex.org/W1986988571","https://openalex.org/W2031168798","https://openalex.org/W2032478287","https://openalex.org/W2084445302","https://openalex.org/W2088236813","https://openalex.org/W2130737785","https://openalex.org/W2134564077","https://openalex.org/W2146271262","https://openalex.org/W2177509960","https://openalex.org/W2509100468","https://openalex.org/W4245698593","https://openalex.org/W4299390900","https://openalex.org/W6658298735"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2086397253","https://openalex.org/W2912321008","https://openalex.org/W2133122801","https://openalex.org/W1998607122","https://openalex.org/W600422426","https://openalex.org/W2324368075","https://openalex.org/W2972124131","https://openalex.org/W2007156430","https://openalex.org/W338149487"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,41,65],"deal":[4],"with":[5],"continuous":[6,56,81],"multi-utility":[7,57,82],"representations":[8],"for":[9],"closed":[10,46,69],"preorders.":[11],"We":[12],"introduce":[13],"the":[14,22,60],"definition":[15],"of":[16,24],"a":[17,25,30,49,55,72,80],"net-compact":[18,50,75],"topology,":[19],"which":[20],"generalizes":[21],"concept":[23],"sequentially":[26,31],"compact":[27,32],"topology.":[28],"Indeed,":[29],"and":[33,74],"first":[34],"countable":[35],"topological":[36,52,77],"space":[37,53,78],"is":[38,62],"net-compact.":[39],"First,":[40],"show":[42],"that":[43,67],"if":[44],"every":[45,68],"preorder":[47,70],"on":[48,71],"Hausdorff":[51,76],"has":[54],"representation,":[58],"then":[59],"topology":[61],"normal.":[63],"Second,":[64],"prove":[66],"normal":[73],"admits":[79],"representation.":[83]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-06T13:50:29.536080","created_date":"2025-10-10T00:00:00"}
