{"title":"关于博尔苏克的非撤回定理","authors":"Waldemar Sieg","doi":"arxiv-2407.13395","DOIUrl":null,"url":null,"abstract":"The classical Borsuk's non-retract theorem asserts that a unit sphere in\n$\\mathbb{R}^n$ is not a continuous retract of the unit closed ball. We will\nshow that such a unit sphere is a piecewise continuous retract of the unit\nclosed ball.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"18 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Borsuk's non-retract theorem\",\"authors\":\"Waldemar Sieg\",\"doi\":\"arxiv-2407.13395\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The classical Borsuk's non-retract theorem asserts that a unit sphere in\\n$\\\\mathbb{R}^n$ is not a continuous retract of the unit closed ball. We will\\nshow that such a unit sphere is a piecewise continuous retract of the unit\\nclosed ball.\",\"PeriodicalId\":501145,\"journal\":{\"name\":\"arXiv - MATH - Classical Analysis and ODEs\",\"volume\":\"18 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Classical Analysis and ODEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.13395\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.13395","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The classical Borsuk's non-retract theorem asserts that a unit sphere in
$\mathbb{R}^n$ is not a continuous retract of the unit closed ball. We will
show that such a unit sphere is a piecewise continuous retract of the unit
closed ball.
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