Proof.r2o(X;Y)meansthatthereissome:X!Ysatisfyingr(x)=kxk(x)forallx2X - PDF document

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Uploaded On 2015-07-27

Proof.r2o(X;Y)meansthatthereissome:X!Ysatisfyingr(x)=kxk(x)forallx2X - PPT Presentation

kwkfww600w0forwhichwehaverfwkwkww2WIfkwkthenkwkckfwkButfw0asw0andbecauseiscontinuousat0wegetthatfw00asw0Sotheaboveinequalitygivesusw0asw0As0 ID: 94369

kwk(f(w))w6=00w=0;forwhichwehave(rf)(w)=kwk(w);w2W:Ifkwk thenk(w)kck(f(w))k.Butf(w)!0asw!0 andbecauseiscontinuousat0wegetthat(f(w))!(0)=0asw!0.Sotheaboveinequalitygivesus(w)!0asw!0.As(0)=

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