# Is C^1[0,1] linearly homeomorphic to C[0,1] ? [closed]

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 JohnsonJan 11 '11 at 18:47

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Mr Smith, you definitely have Slavic roots: "gomeomorphic" gives yourself completely... Can't you put more effort on your question? It sounds a homework. –  Wadim Zudilin Jan 8 '11 at 12:48
Dear Mr Smith, Wadim was merely suggesting what you could have already read here, mathoverflow.net/howtoask –  Gjergji Zaimi Jan 8 '11 at 13:07
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.