 In 1995, Luis Rodríguez-Piazza proved that the isometry can be chosen so that every non-zero function in the image is nowhere differentiable.Put another way, if consists of functions that are differentiable at at least one point of , then can be chosen so that This conclusion applies to the space itself, hence there exists a linear map that is an isometry onto its image, such that image under of (the subspace consisting of functions that are everywhere differentiable with continuous derivative) intersects only at