{"id":"https://openalex.org/W2065250257","doi":"https://doi.org/10.1017/s0960129597002338","title":"When Scott is weak on the top","display_name":"When Scott is weak on the top","publication_year":1997,"publication_date":"1997-10-01","ids":{"openalex":"https://openalex.org/W2065250257","doi":"https://doi.org/10.1017/s0960129597002338","mag":"2065250257"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129597002338","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129597002338","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058087229","display_name":"Abbas Edalat","orcid":"https://orcid.org/0000-0002-6211-1991"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"ABBAS EDALAT","raw_affiliation_strings":["Department of Computing, Imperial College, 180 Queen's gate, London SW7 2BZ. Email:","Department of Computing, Imperial College, 180 Queen's gate, London SW7 2BZ. Email: ae@doc.ic.ac.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computing, Imperial College, 180 Queen's gate, London SW7 2BZ. Email:","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Department of Computing, Imperial College, 180 Queen's gate, London SW7 2BZ. Email: ae@doc.ic.ac.uk#TAB#","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058087229"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":5.2786,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.96267653,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"7","issue":"5","first_page":"401","last_page":"417"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.995199978351593,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.995199978351593,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9271000027656555,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9259999990463257,"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/mathematics","display_name":"Mathematics","score":0.7336784601211548},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5999827980995178},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5897216796875},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5456221699714661},{"id":"https://openalex.org/keywords/fisher-information-metric","display_name":"Fisher information metric","score":0.5338690280914307},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.5330836772918701},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4780474305152893},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.47622615098953247},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.4674195945262909},{"id":"https://openalex.org/keywords/complete-metric-space","display_name":"Complete metric space","score":0.45751211047172546},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4515766203403473},{"id":"https://openalex.org/keywords/metric-differential","display_name":"Metric differential","score":0.43983757495880127},{"id":"https://openalex.org/keywords/injective-metric-space","display_name":"Injective metric space","score":0.38830697536468506},{"id":"https://openalex.org/keywords/intrinsic-metric","display_name":"Intrinsic metric","score":0.3630419969558716},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3225322365760803},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3015492260456085},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21045443415641785},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13217264413833618}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7336784601211548},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5999827980995178},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5897216796875},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5456221699714661},{"id":"https://openalex.org/C127104897","wikidata":"https://www.wikidata.org/wiki/Q5454858","display_name":"Fisher information metric","level":4,"score":0.5338690280914307},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.5330836772918701},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4780474305152893},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.47622615098953247},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.4674195945262909},{"id":"https://openalex.org/C93361540","wikidata":"https://www.wikidata.org/wiki/Q848569","display_name":"Complete metric space","level":3,"score":0.45751211047172546},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4515766203403473},{"id":"https://openalex.org/C146562557","wikidata":"https://www.wikidata.org/wiki/Q1925669","display_name":"Metric differential","level":5,"score":0.43983757495880127},{"id":"https://openalex.org/C177547787","wikidata":"https://www.wikidata.org/wiki/Q6034319","display_name":"Injective metric space","level":3,"score":0.38830697536468506},{"id":"https://openalex.org/C41261874","wikidata":"https://www.wikidata.org/wiki/Q3855712","display_name":"Intrinsic metric","level":4,"score":0.3630419969558716},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3225322365760803},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3015492260456085},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21045443415641785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13217264413833618},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0960129597002338","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129597002338","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.37.2803","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.2803","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eecs.umich.edu/~klavins/hsrg/rounds/scottopweak.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.49.3150","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.3150","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.doc.ic.ac.uk/~ae/papers/weakfull.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W642374273","https://openalex.org/W650925811","https://openalex.org/W1224113374","https://openalex.org/W1492711856","https://openalex.org/W1512502927","https://openalex.org/W1979684610","https://openalex.org/W1980591506","https://openalex.org/W1984190214","https://openalex.org/W1997766149","https://openalex.org/W2028924965","https://openalex.org/W2051573991","https://openalex.org/W2056099894","https://openalex.org/W2082241908","https://openalex.org/W2115154197","https://openalex.org/W2155748644","https://openalex.org/W2520815221","https://openalex.org/W3096424428"],"related_works":["https://openalex.org/W4363675004","https://openalex.org/W2947185879","https://openalex.org/W2987243377","https://openalex.org/W2048731283","https://openalex.org/W4255883801","https://openalex.org/W2398868469","https://openalex.org/W2565930412","https://openalex.org/W2913616026","https://openalex.org/W2381341335","https://openalex.org/W2795812777"],"abstract_inverted_index":{"We":[0,28,130,141],"construct":[1],"an":[2,44,85,93,143],"approximating":[3],"chain":[4,95],"of":[5,12,43,54,57,71,75,80,88,96,103,114,150,162],"simple":[6],"valuations":[7,98],"on":[8,24,99,119],"the":[9,25,52,58,63,72,76,81,100,111,120,147,158,163,167],"upper":[10,101],"space":[11,16,35,53,60,102,121],"a":[13,20,32,39,69,89,104,132],"compact":[14,105],"metric":[15,26,34,59,106],"whose":[17],"lub":[18],"is":[19,36,66],"given":[21,128],"probability":[22,55,90],"measure":[23,91,161],"space.":[27],"show":[29,109],"that":[30,110],"whenever":[31],"separable":[33],"homeomorphic":[37,67],"to":[38,126,145,157,171],"G":[40],"\u03b4":[41],"subset":[42,70],"\u03c9-continuous":[45,82],"dcpo":[46],"equipped":[47,61],"with":[48,62,68,155],"its":[49],"Scott":[50],"topology,":[51],"measures":[56],"weak":[64],"topology":[65],"maximal":[73],"elements":[74],"probabilistic":[77],"power":[78],"domain":[79],"dcpo.":[83],"Given":[84],"effective":[86],"approximation":[87],"by":[92],"increasing":[94],"normalised":[97],"space,":[107],"we":[108],"expected":[112,148],"value":[113,149],"any":[115,127,151],"H\u00f6lder":[116,152],"continuous":[117,153],"function":[118,154],"can":[122],"be":[123],"obtained":[124],"up":[125],"accuracy.":[129],"present":[131],"novel":[133],"application":[134],"in":[135,138,166],"computing":[136],"integrals":[137],"dynamical":[139],"systems.":[140],"obtain":[142],"algorithm":[144],"compute":[146],"respect":[156],"unique":[159],"invariant":[160],"Feigenbaum":[164],"map":[165],"periodic":[168],"doubling":[169],"route":[170],"chaos.":[172]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}