Geodesic
A~continuously differentiable discontinuous function on the space~$D$
Izvestiya. Mathematics , Tome 59 (1995) no. 5, pp. 1077-1082.

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By explicit formula we define a real valued everywhere discontinuous function on the Schwartz space $D$ (of infinitely differentiable functions with compact support) that has continuous Frechet derivatives of all orders (which are defined everywhere). 
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M. O. Smolyanova. A~continuously differentiable discontinuous function on the space~$D$. Izvestiya. Mathematics , Tome 59 (1995) no. 5, pp. 1077-1082. http://geodesic.mathdoc.fr/item/IM2_1995_59_5_a10/

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