{"title":"Mappings from S3 to S2 whose point inverses Have the shape of a circle","authors":"D.S. Coram , P.F. Duvall Jr.","doi":"10.1016/0016-660X(79)90037-0","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>f</em>:<em>S</em><sup>3</sup>→<em>S</em><sup>2</sup> be a continuous function. If <em>y</em>ϵ<em>S</em><sup>2</sup> assume that <em>f</em><sup>-1</sup> (<em>y</em>) has the shape of a circle and that there are neighborhoods <em>V</em> ⊂ <em>U</em> of <em>f</em><sup>-1</sup>(<em>y</em>) such that for any point inverse <em>f</em><sup>-1</sup>(<em>z</em>)⊂<em>V</em>, the inclusion of <em>f</em><sup>-1</sup>(<em>z</em>) into <em>U</em> is essential. We show that <em>f</em> can be approximated arbitrarily closely by Seifert fiber maps.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 3","pages":"Pages 239-246"},"PeriodicalIF":0.0000,"publicationDate":"1979-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90037-0","citationCount":"21","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Topology and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0016660X79900370","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 21
Abstract
Let f:S3→S2 be a continuous function. If yϵS2 assume that f-1 (y) has the shape of a circle and that there are neighborhoods V ⊂ U of f-1(y) such that for any point inverse f-1(z)⊂V, the inclusion of f-1(z) into U is essential. We show that f can be approximated arbitrarily closely by Seifert fiber maps.
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