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26CHAPTER3.CONTRACTIONSApointx2XiscalledanaccumulationpointofasetAXif 26CHAPTER3.CONTRACTIONSApointx2XiscalledanaccumulationpointofasetAXif

26CHAPTER3.CONTRACTIONSApointx2XiscalledanaccumulationpointofasetAXif - PDF document

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Uploaded On 2016-03-08

26CHAPTER3.CONTRACTIONSApointx2XiscalledanaccumulationpointofasetAXif - PPT Presentation

1KdFxxandKn0asn1Inthelaststepweusedthefactthatwith0K1itfollowsthatmn1Xk0Kk1Xk0Kk1 1KThusthelimitlimn1FnxexistsbecauseCauchysequencesconvergeinXWedenotethelimitx0By322underit ID: 247866

1Kd(F(x);x)andKn!0asn!1.Inthelaststepweusedthefactthatwith0K1itfollowsthatmn1Xk=0Kk1Xk=0Kk=1 1K:Thusthelimitlimn!1Fn(x)existsbecauseCauchysequencesconvergeinX.Wedenotethelimitx0.By(3.2.2)underit

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