Sur un exemple de Banach et Kuratowski

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Title

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For A ⊂ I = [0,1], let

L_{A}

be the set of continuous real-valued functions on I which vanish on a neighborhood of A. We prove that if A is an analytic subset which is not an

F_{σ}

and whose closure has an empty interior, then

L_{A}

is homeomorphic to the space of differentiable functions from I into ℝ.

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