{"id":"https://openalex.org/W2090440866","doi":"https://doi.org/10.1016/s1571-0661(04)80772-2","title":"The complexity space of a valued linearly ordered set","display_name":"The complexity space of a valued linearly ordered set","publication_year":2003,"publication_date":"2003-10-01","ids":{"openalex":"https://openalex.org/W2090440866","doi":"https://doi.org/10.1016/s1571-0661(04)80772-2","mag":"2090440866"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(04)80772-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80772-2","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1016/s1571-0661(04)80772-2","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008660700","display_name":"Salvador Romaguera","orcid":"https://orcid.org/0000-0001-7857-6139"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"S. Romaguera","raw_affiliation_strings":["Escuela de Caminos, Departamento de matema\u00e1tica Aplicada, Universidad Polit\u00e9cnica de Valencia, 46071 Valencia, Spain"],"affiliations":[{"raw_affiliation_string":"Escuela de Caminos, Departamento de matema\u00e1tica Aplicada, Universidad Polit\u00e9cnica de Valencia, 46071 Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059955897","display_name":"Enrique A. S\u00e1nchez\u2010P\u00e9rez","orcid":"https://orcid.org/0000-0001-8854-3154"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"E.A. S\u00e1nchez-P\u00e9rez","raw_affiliation_strings":["Escuela de Caminos, Departamento de matema\u00e1tica Aplicada, Universidad Polit\u00e9cnica de Valencia, 46071 Valencia, Spain"],"affiliations":[{"raw_affiliation_string":"Escuela de Caminos, Departamento de matema\u00e1tica Aplicada, Universidad Polit\u00e9cnica de Valencia, 46071 Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007428198","display_name":"\u00d3scar Valero","orcid":"https://orcid.org/0000-0003-4710-1338"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"O. Valero","raw_affiliation_strings":["Escuela de Caminos, Departamento de matema\u00e1tica Aplicada, Universidad Polit\u00e9cnica de Valencia, 46071 Valencia, Spain"],"affiliations":[{"raw_affiliation_string":"Escuela de Caminos, Departamento de matema\u00e1tica Aplicada, Universidad Polit\u00e9cnica de Valencia, 46071 Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007428198","https://openalex.org/A5008660700","https://openalex.org/A5059955897"],"corresponding_institution_ids":["https://openalex.org/I60053951"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.18873099,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"74","issue":null,"first_page":"158","last_page":"171"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9987999796867371,"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":0.9987999796867371,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9962999820709229,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9919000267982483,"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/mathematics","display_name":"Mathematics","score":0.7864996790885925},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5621616840362549},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5514852404594421},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5436233282089233},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.4550850987434387},{"id":"https://openalex.org/keywords/valuation","display_name":"Valuation (finance)","score":0.4481842815876007},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.42614060640335083},{"id":"https://openalex.org/keywords/linear-space","display_name":"Linear space","score":0.4146004617214203},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33834630250930786},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11650350689888},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0858314037322998}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7864996790885925},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5621616840362549},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5514852404594421},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5436233282089233},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.4550850987434387},{"id":"https://openalex.org/C186027771","wikidata":"https://www.wikidata.org/wiki/Q4008379","display_name":"Valuation (finance)","level":2,"score":0.4481842815876007},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.42614060640335083},{"id":"https://openalex.org/C176370821","wikidata":"https://www.wikidata.org/wiki/Q1826459","display_name":"Linear space","level":2,"score":0.4146004617214203},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33834630250930786},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11650350689888},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0858314037322998},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s1571-0661(04)80772-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80772-2","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(04)80772-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80772-2","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W16080872","https://openalex.org/W63176152","https://openalex.org/W72558488","https://openalex.org/W568516392","https://openalex.org/W647882146","https://openalex.org/W1557973150","https://openalex.org/W1559626229","https://openalex.org/W1988206529","https://openalex.org/W2025926772","https://openalex.org/W2047277075","https://openalex.org/W2075925569","https://openalex.org/W2081233506","https://openalex.org/W2095137273","https://openalex.org/W2110149567","https://openalex.org/W2742381852","https://openalex.org/W4212901846","https://openalex.org/W4234716205","https://openalex.org/W4285719527","https://openalex.org/W6600663381","https://openalex.org/W6633471653"],"related_works":["https://openalex.org/W4237277701","https://openalex.org/W2121424666","https://openalex.org/W4301250310","https://openalex.org/W2055420561","https://openalex.org/W2067700950","https://openalex.org/W1669998927","https://openalex.org/W4301895170","https://openalex.org/W3162039195","https://openalex.org/W2163760347","https://openalex.org/W2121793128"],"abstract_inverted_index":{"By":[0],"a":[1,12,20,40,48,74,93,110],"valued":[2,34],"linearly":[3,21],"ordered":[4,22],"set":[5,23],"(a":[6],"VLOS":[7,38,44,75,111],"for":[8,96],"short),":[9],"we":[10,103,122],"mean":[11],"pair":[13],"(X,":[14,45,67,112,134],"\u03d5)":[15,46,68,113],"such":[16],"that":[17,62,124,158],"X":[18,54],"is":[19,26,39,57,126],"and":[24,114,128,147],"\u03d5":[25],"strictly":[27],"increasing":[28],"(=":[29],"positive":[30],"monotone)":[31],"nonnegative":[32],"real":[33,145],"function.":[35],"Clearly,":[36],"any":[37],"valuation":[41],"space.":[42],"Each":[43],"generates":[47],"linear":[49],"weightable":[50,127],"quasi-metric":[51],"d\u03d5":[52],"on":[53],"whose":[55],"conjugate":[56],"order":[58],"preserving.":[59],"We":[60,136],"show":[61,123],"the":[63,71,78,86,97,105,133,142,160],"Smyth":[64,130],"completion":[65],"of":[66,73,88,100,109,117,132,144,151],"also":[69],"admits":[70],"structure":[72],".":[76],"On":[77],"other":[79],"hand,":[80],"M.":[81],"Schellekens":[82],"introduced":[83],"in":[84],"1995,":[85],"theory":[87],"complexity":[89,98,107,139],"spaces":[90],"to":[91,141,156],"develop":[92],"topological":[94],"foundation":[95],"analysis":[99],"programs.":[101],"Here,":[102],"introduce":[104],"so-called":[106],"space":[108],"discuss":[115,148],"some":[116,149],"its":[118],"properties.":[119],"In":[120],"particular,":[121],"it":[125],"preserves":[129],"completeness":[131],"\u03d5).":[135],"apply":[137],"this":[138],"approach":[140],"measurement":[143],"numbers":[146],"advantages":[150],"our":[152],"methods":[153],"with":[154],"respect":[155],"those":[157],"use":[159],"classical":[161],"Baire":[162],"metric.":[163]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
