2CLAYSHONKWILERProof.Supposejisnulhomotopic.LetH:SnI!Rn+1nf0gbeaho-mo - PDF document

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Uploaded On 2017-11-25

2CLAYSHONKWILERProof.Supposejisnulhomotopic.LetH:SnI!Rn+1nf0gbeaho-mo - PPT Presentation

jjxjjThenrisaretractionofRn1nf0gontoSnasweveshowninclassNowdeneH0SnISnbyH0xtrHxtThensinceHisahomotopybetweenjandaconstantmapH0iscontinuousandforallx2SnH0x0rHx0rHx ID: 609176

jjxjj:ThenrisaretractionofRn+1nf0gontoSn aswe'veshowninclass.Now deneH0:SnI!SnbyH0(x;t)=(rH)(x;t):Then sinceHisahomotopybetweenjandaconstantmap H0iscontinuousand forallx2Sn H0(x;0)=(rH)(x;0)=r(H(x

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