{"title":"AR associated with ANR-sequence and shape","authors":"Y. Kodama, J. Ono, T. Watanabe","doi":"10.1016/0016-660X(78)90052-1","DOIUrl":null,"url":null,"abstract":"<div><p>For a given ANR-sequence (<strong><em>X,A</em></strong>) associated with a par (<em>X,A</em>) of compacta, a pair (<em>N</em>(<strong><em>X</em></strong>),<em>N</em>(<strong><em>A</em></strong>)) of compact AR's containing (<em>X,A</em>) as an unstable pair is constructed. The weak proper homotopy type of the pair (<em>N</em>(<strong><em>X</em></strong>)-',<em>N</em>(<strong><em>A</em></strong>)-<em>A</em>) determines the shape of (<em>X,A</em>) in the sense of Mardešić and Segal. Several applications of this result are given. A cohomological version of the Whitehead theorem in shape theory is proved.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"9 2","pages":"Pages 71-88"},"PeriodicalIF":0.0000,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90052-1","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Topology and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0016660X78900521","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 8
Abstract
For a given ANR-sequence (X,A) associated with a par (X,A) of compacta, a pair (N(X),N(A)) of compact AR's containing (X,A) as an unstable pair is constructed. The weak proper homotopy type of the pair (N(X)-',N(A)-A) determines the shape of (X,A) in the sense of Mardešić and Segal. Several applications of this result are given. A cohomological version of the Whitehead theorem in shape theory is proved.
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