{"id":"https://openalex.org/W2335648564","doi":"https://doi.org/10.2307/1968911","title":"Continuous Mappings of Infinite Polyhedra","display_name":"Continuous Mappings of Infinite Polyhedra","publication_year":1941,"publication_date":"1941-04-01","ids":{"openalex":"https://openalex.org/W2335648564","doi":"https://doi.org/10.2307/1968911","mag":"2335648564"},"language":"en","primary_location":{"id":"doi:10.2307/1968911","doi":"https://doi.org/10.2307/1968911","is_oa":false,"landing_page_url":"https://doi.org/10.2307/1968911","pdf_url":null,"source":{"id":"https://openalex.org/S45918994","display_name":"Annals of Mathematics","issn_l":"0003-486X","issn":["0003-486X","1939-8980"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310316273","host_organization_name":"Princeton University","host_organization_lineage":["https://openalex.org/P4310316273"],"host_organization_lineage_names":["Princeton University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Mathematics","raw_type":"journal-article"},"volume":null,"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/A5064204497","display_name":"Samuel Eilenberg","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Samuel Eilenberg","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5064204497"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.395,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"42","issue":"2","first_page":"459","last_page":"459"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9154999852180481,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9154999852180481,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.07240000367164612,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.00139999995008111,"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/infinite-chains","display_name":"infinite chains","score":0.7419999837875366},{"id":"https://openalex.org/keywords/cohomology","display_name":"cohomology","score":0.8510000109672546},{"id":"https://openalex.org/keywords/homology","display_name":"homology","score":0.7429999709129333},{"id":"https://openalex.org/keywords/sphere","display_name":"sphere","score":0.5609999895095825}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.8860131502151489},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8793317079544067},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.398732453584671},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3461097478866577}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/1968911","doi":"https://doi.org/10.2307/1968911","is_oa":false,"landing_page_url":"https://doi.org/10.2307/1968911","pdf_url":null,"source":{"id":"https://openalex.org/S45918994","display_name":"Annals of Mathematics","issn_l":"0003-486X","issn":["0003-486X","1939-8980"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310316273","host_organization_name":"Princeton University","host_organization_lineage":["https://openalex.org/P4310316273"],"host_organization_lineage_names":["Princeton University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2916043681","https://openalex.org/W2896131632","https://openalex.org/W2391438543","https://openalex.org/W2997473813","https://openalex.org/W2008231869","https://openalex.org/W2551069560","https://openalex.org/W1594091061","https://openalex.org/W2522231841","https://openalex.org/W2327310844","https://openalex.org/W4250631474"],"abstract_inverted_index":{"This":[0],"paper":[1,178],"is":[2,40,49,54,81,83,99,101,116,159,164],"concerned":[3],"with":[4],"some":[5],"special":[6],"cases":[7,148],"of":[8,12,17,20,32,58,109,127,176,187,199],"the":[9,14,36,50,64,72,107,125,137,147,150],"general":[10,121],"problem":[11,37,131],"determining":[13],"homotopy":[15],"classes":[16],"continuous":[18],"mappings":[19],"a":[21,25,41,61,104,119,153,184],"polyhedron":[22,44],"K":[23,39,80,98,163],"into":[24],"space":[26,122],"Y.":[27,123],"The":[28,52,77,95,197],"well":[29],"known":[30],"theorem":[31,151],"H.":[33],"Hopf":[34],"solves":[35],"when":[38,149,162],"finite":[42,82,165],"n-dimensional":[43,100],"and":[45,89,135,142],"Y":[46],"=":[47],"Sn":[48,115],"n-sphere.":[51],"solution":[53],"given":[55,193],"in":[56,71,129,146,194,208],"terms":[57],"homology.":[59],"In":[60],"recent":[62],"paper'":[63],"author":[65],"has":[66,152],"generalized":[67],"Hopf's":[68],"result":[69],"simultaneously":[70],"following":[73],"three":[74],"directions:":[75],"(a)":[76],"hypothesis":[78,96,105],"that":[79,97],"removed":[84],"by":[85,103,118],"admitting":[86],"infinite":[87,188],"chains":[88],"letting":[90],"cohomologies":[91,128],"replace":[92],"homologies.":[93],"(b)":[94],"replaced":[102,117],"concerning":[106],"vanishing":[108],"certain":[110],"higher-dimensional":[111],"cohomology":[112],"groups.":[113],"(c)":[114],"more":[120,140],"Although":[124],"use":[126],"this":[130,177],"seems":[132],"quite":[133],"natural":[134],"justified,":[136],"results":[138,198],"become":[139],"intuitive":[141],"easier":[143],"to":[144,170],"apply":[145],"homological":[154],"interpretation.":[155],"Such":[156],"an":[157,181],"interpretation":[158,182],"easily":[160],"available":[161],"but":[166],"does":[167],"not":[168],"seem":[169],"be":[171],"possible":[172],"generally.":[173],"Section":[174],"2":[175],"gives":[179],"such":[180],"for":[183],"large":[185],"class":[186],"polyhedra.":[189],"Various":[190],"applications":[191],"are":[192,202,206],"sections":[195],"3-10.":[196],"CM":[200],"which":[201],"being":[203],"used":[204],"here":[205],"collected":[207],"section":[209],"1.":[210]},"counts_by_year":[],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}
