Is $C^1[0,1]$ linearly homeomorphic to $C[0,1]$ ?
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closed as too localized by Andres Caicedo, Yemon Choi, Harry Gindi, Wadim Zudilin, Bill Johnson Jan 11 '11 at 18:47This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question. 


By integration, $C[0,1]$ is linearly homeomorphic to a hyperplane in $C^1[0,1]$. For example, all elements $g$ of $C^1[0,1]$ with $g(0)=0$. All classical Banach spaces are linearly isomorphic to their hyperplanes. In this case it can be proved constructively. So, Mr Smith, onevisit wonder: Is this your homework? 

