{"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}
引用次数: 0
Abstract
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.