{"title":"On shape of product spaces","authors":"Yukihiro Kodama","doi":"10.1016/0016-660X(78)90045-4","DOIUrl":null,"url":null,"abstract":"<div><p>It is known that if <em>X</em> is a compactum and <em>Y</em> is metrizable Sh<sub>5</sub>(<em>X</em> × <em>Y</em>) is not generally determined by Sh<sub>5</sub>(<em>X</em>) and Sh<sub>5</sub>(<em>Y</em>), where Sh<sub>5</sub>(<em>Z</em>) is the strong shape of <em>Z</em> in the sense of Borsuk. In this paper it is proved that Sh(<em>X</em> × <em>Y</em>) is uniquely determined by Sh(<em>X</em>) and Sh(<em>Y</em>), where Sh(<em>Z</em>) is the shape of <em>Z</em> in the sense of Fox. If <em>X</em> is an FANR and <em>Y</em> is an MANR, then <em>X</em> × <em>Y</em> is an MANR.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"8 2","pages":"Pages 141-150"},"PeriodicalIF":0.0000,"publicationDate":"1978-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(78)90045-4","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Topology and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0016660X78900454","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
It is known that if X is a compactum and Y is metrizable Sh5(X × Y) is not generally determined by Sh5(X) and Sh5(Y), where Sh5(Z) is the strong shape of Z in the sense of Borsuk. In this paper it is proved that Sh(X × Y) is uniquely determined by Sh(X) and Sh(Y), where Sh(Z) is the shape of Z in the sense of Fox. If X is an FANR and Y is an MANR, then X × Y is an MANR.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
