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For the Frechet space E=C^{\infty}(S^1) and for a smooth \phi: R to R, weprove that the associated map E to E given by x mapsto\phi\circ x satisfies thecontinuous B\Gamma--differentiability condition in Yamamuro's inverse functiontheorem only if \phi is affine. Via more complicated examples, we alsogenerally discuss the importance of testing the applicability of proposedinverse and implicit function theorems by this kind of simple maps.

On Yamamuro's inverse and implicit function theorems in terms of calibrations