{"title":"横截面简单的球体可以很狂野","authors":"R.J. Daverman , S.A. Pax","doi":"10.1016/0016-660X(79)90003-5","DOIUrl":null,"url":null,"abstract":"<div><p>The first part of this paper supplements earlier work of the first-named author by exhibiting an example of a wild <em>n</em>-sphere <em>Σ</em> in <em>E</em><sup><em>n</em>+1</sup> (<em>n</em>⩾4) for which each horizontal <em>n</em>-dimensional hyperplane of <em>E</em><sup><em>n</em>+1</sup> that does meet <em>Σ</em> intersects it either in a point or in an (<em>n</em> − 1)-sphere that is flatly embedded in the hyperplane. The second part sets forth an improved criterion for detecting the <em>n</em>-cell (<em>n</em> ≠ 4) based upon properties of slices determined as inverse sets associated with maps of a space to an interval.</p></div>","PeriodicalId":100574,"journal":{"name":"General Topology and its Applications","volume":"10 2","pages":"Pages 139-146"},"PeriodicalIF":0.0000,"publicationDate":"1979-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0016-660X(79)90003-5","citationCount":"3","resultStr":"{\"title\":\"Cross sectionally simple spheres can be wild\",\"authors\":\"R.J. Daverman , S.A. Pax\",\"doi\":\"10.1016/0016-660X(79)90003-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The first part of this paper supplements earlier work of the first-named author by exhibiting an example of a wild <em>n</em>-sphere <em>Σ</em> in <em>E</em><sup><em>n</em>+1</sup> (<em>n</em>⩾4) for which each horizontal <em>n</em>-dimensional hyperplane of <em>E</em><sup><em>n</em>+1</sup> that does meet <em>Σ</em> intersects it either in a point or in an (<em>n</em> − 1)-sphere that is flatly embedded in the hyperplane. The second part sets forth an improved criterion for detecting the <em>n</em>-cell (<em>n</em> ≠ 4) based upon properties of slices determined as inverse sets associated with maps of a space to an interval.</p></div>\",\"PeriodicalId\":100574,\"journal\":{\"name\":\"General Topology and its Applications\",\"volume\":\"10 2\",\"pages\":\"Pages 139-146\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1979-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0016-660X(79)90003-5\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"General Topology and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0016660X79900035\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Topology and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0016660X79900035","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The first part of this paper supplements earlier work of the first-named author by exhibiting an example of a wild n-sphere Σ in En+1 (n⩾4) for which each horizontal n-dimensional hyperplane of En+1 that does meet Σ intersects it either in a point or in an (n − 1)-sphere that is flatly embedded in the hyperplane. The second part sets forth an improved criterion for detecting the n-cell (n ≠ 4) based upon properties of slices determined as inverse sets associated with maps of a space to an interval.
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