{"id":"https://openalex.org/W2026776098","doi":"https://doi.org/10.1017/s0960129506005895","title":"Two preservation results for countable products of sequential spaces","display_name":"Two preservation results for countable products of sequential spaces","publication_year":2007,"publication_date":"2007-02-01","ids":{"openalex":"https://openalex.org/W2026776098","doi":"https://doi.org/10.1017/s0960129506005895","mag":"2026776098"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129506005895","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129506005895","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":true,"oa_status":"green","oa_url":"https://www.research.ed.ac.uk/en/publications/34ade931-012d-4802-9c07-e14f2a9e4f89","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100638436","display_name":"Matthias Schr\u00f6der","orcid":"https://orcid.org/0009-0007-4295-0230"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"MATTHIAS SCHR\u00d6DER","raw_affiliation_strings":["LFCS, School of Informatics, University of Edinburgh, U.K. Email:","LFCS, School of Informatics, University of Edinburgh, U.K. Email: mschrode@inf.ed.ac.uk, alex.simpson@ed.ac.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"LFCS, School of Informatics, University of Edinburgh, U.K. Email:","institution_ids":["https://openalex.org/I98677209"]},{"raw_affiliation_string":"LFCS, School of Informatics, University of Edinburgh, U.K. Email: mschrode@inf.ed.ac.uk, alex.simpson@ed.ac.uk#TAB#","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110256373","display_name":"Alex Simpson","orcid":null},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"ALEX SIMPSON","raw_affiliation_strings":["LFCS, School of Informatics, University of Edinburgh, U.K. Email:","LFCS, School of Informatics, University of Edinburgh, U.K. Email: mschrode@inf.ed.ac.uk, alex.simpson@ed.ac.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"LFCS, School of Informatics, University of Edinburgh, U.K. Email:","institution_ids":["https://openalex.org/I98677209"]},{"raw_affiliation_string":"LFCS, School of Informatics, University of Edinburgh, U.K. Email: mschrode@inf.ed.ac.uk, alex.simpson@ed.ac.uk#TAB#","institution_ids":["https://openalex.org/I98677209"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100638436"],"corresponding_institution_ids":["https://openalex.org/I98677209"],"apc_list":null,"apc_paid":null,"fwci":1.4973,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82095123,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"17","issue":"1","first_page":"161","last_page":"172"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9997000098228455,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9997000098228455,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.835064172744751},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.787366509437561},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5726711750030518},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5662497282028198},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.5322107076644897},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.5300887227058411},{"id":"https://openalex.org/keywords/compact-open-topology","display_name":"Compact-open topology","score":0.5289321541786194},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.49602851271629333},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.48648616671562195},{"id":"https://openalex.org/keywords/product-topology","display_name":"Product topology","score":0.45859163999557495},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4547842741012573},{"id":"https://openalex.org/keywords/baire-space","display_name":"Baire space","score":0.42375048995018005},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4225616455078125},{"id":"https://openalex.org/keywords/subcategory","display_name":"Subcategory","score":0.4195573925971985},{"id":"https://openalex.org/keywords/topological-tensor-product","display_name":"Topological tensor product","score":0.2979702353477478},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.150831401348114},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06009584665298462},{"id":"https://openalex.org/keywords/functional-analysis","display_name":"Functional analysis","score":0.05805957317352295}],"concepts":[{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.835064172744751},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.787366509437561},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5726711750030518},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5662497282028198},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.5322107076644897},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5300887227058411},{"id":"https://openalex.org/C6419321","wikidata":"https://www.wikidata.org/wiki/Q1669863","display_name":"Compact-open topology","level":5,"score":0.5289321541786194},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.49602851271629333},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48648616671562195},{"id":"https://openalex.org/C123222754","wikidata":"https://www.wikidata.org/wiki/Q1070472","display_name":"Product topology","level":2,"score":0.45859163999557495},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4547842741012573},{"id":"https://openalex.org/C166359235","wikidata":"https://www.wikidata.org/wiki/Q1150180","display_name":"Baire space","level":2,"score":0.42375048995018005},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4225616455078125},{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.4195573925971985},{"id":"https://openalex.org/C178099376","wikidata":"https://www.wikidata.org/wiki/Q7825044","display_name":"Topological tensor product","level":4,"score":0.2979702353477478},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.150831401348114},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06009584665298462},{"id":"https://openalex.org/C55112680","wikidata":"https://www.wikidata.org/wiki/Q190549","display_name":"Functional analysis","level":3,"score":0.05805957317352295},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0960129506005895","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129506005895","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:pure.ed.ac.uk:openaire/34ade931-012d-4802-9c07-e14f2a9e4f89","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/34ade931-012d-4802-9c07-e14f2a9e4f89","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Schr\u00f6der, M & Simpson, A 2007, 'Two preservation results for countable products of sequential spaces', Mathematical Structures in Computer Science, vol. 17, no. 1, pp. 161-172. https://doi.org/10.1017/S0960129506005895","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.6282","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.6282","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dcs.ed.ac.uk/home/als/Research/Sources/prodpres.pdf","raw_type":"text"},{"id":"pmh:oai:pure.ed.ac.uk:publications/34ade931-012d-4802-9c07-e14f2a9e4f89","is_oa":false,"landing_page_url":"https://www.research.ed.ac.uk/portal/en/publications/two-preservation-results-for-countable-products-of-sequential-spaces(34ade931-012d-4802-9c07-e14f2a9e4f89).html","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:pure.ed.ac.uk:openaire/34ade931-012d-4802-9c07-e14f2a9e4f89","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/34ade931-012d-4802-9c07-e14f2a9e4f89","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Schr\u00f6der, M & Simpson, A 2007, 'Two preservation results for countable products of sequential spaces', Mathematical Structures in Computer Science, vol. 17, no. 1, pp. 161-172. https://doi.org/10.1017/S0960129506005895","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W144068439","https://openalex.org/W1509579779","https://openalex.org/W1525647423","https://openalex.org/W1596749189","https://openalex.org/W1823042607","https://openalex.org/W1986005496","https://openalex.org/W2069246348","https://openalex.org/W2149175915","https://openalex.org/W2160234152","https://openalex.org/W2322118446","https://openalex.org/W2601539419","https://openalex.org/W2611511037","https://openalex.org/W2911572548","https://openalex.org/W2913418092","https://openalex.org/W4243563333","https://openalex.org/W4388310169"],"related_works":["https://openalex.org/W1995053131","https://openalex.org/W1986005496","https://openalex.org/W1600012914","https://openalex.org/W2081903545","https://openalex.org/W1566175320","https://openalex.org/W1987292769","https://openalex.org/W1989775214","https://openalex.org/W2114464826","https://openalex.org/W2593417979","https://openalex.org/W4388499860"],"abstract_inverted_index":{"We":[0],"prove":[1],"two":[2],"results":[3,53],"for":[4],"the":[5,30,37,59],"sequential":[6,12,40],"topology":[7],"on":[8,63],"countable":[9,20,50],"products":[10],"of":[11,22,45,61],"topological":[13,23],"spaces.":[14,32,65],"First":[15],"we":[16,34],"show":[17,35],"that":[18,36],"a":[19,26],"product":[21,31],"quotients":[24],"yields":[25],"quotient":[27],"map":[28],"between":[29],"Then":[33],"reflection":[38],"from":[39],"spaces":[41,48],"to":[42,58],"its":[43],"subcategory":[44],"monotone":[46],"\u03c9-convergence":[47],"preserves":[49],"products.":[51],"These":[52],"are":[54],"motivated":[55],"by":[56],"applications":[57],"modelling":[60],"computation":[62],"non-discrete":[64]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
