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Let D (resp. D∗) be the subspace of C = C([0, 1],R) consisting of differentiable functions (resp. of functions differentiable at one point at least). We give topological characterizations of the pairs (C,D) and (C,D∗) and use them to give some examples of spaces homeomorphic to C \ D or to C \ D∗.

Sur deux espaces de fonctions non dérivables