Geodesic
A continuously differentiable discontinuous function on the space $D$
Izvestiya. Mathematics, Tome 59 (1995) no. 5, pp. 1077-1082 Cet article a éte moissonné depuis la source Math-Net.Ru

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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/

[1] Averbukh V. I., Smolyanov O. G., “Razlichnye opredeleniya proizvodnoi v lineinykh topologicheskikh prostranstvakh”, UMN, 23:4 (1968), 67–116 | MR | Zbl

[2] Smolyanov O. G., “Nonclosed sequentially closed subsets of locally convex spaces and applications”, Note di Matematica, 12 (1992), 237–244 | MR | Zbl

[3] Shkarin S. A., “O differentsiruemosti po Gato i nepreryvnosti otobrazhenii”, Sib. matem. zhurn., 1992, no. 5, 176–185 | MR | Zbl

[4] Shefer Kh., Topologicheskie vektornye prostranstva, Mir, M., 1971 | MR

[5] Smolyanov O. G., Analiz na topologicheskikh lineinykh prostranstvakh i ego prilozheniya, Izd-vo MGU, M., 1979

[6] Smolyanova M. O., “Beskonechno differentsiruemye razryvnye funktsii na prostranstve $D'$”, Vestn. Mosk. un-ta. Ser. 1, 1993, no. 1, 49–52 | MR | Zbl

[7] Frölicher A., Kriegl A., Linear spaces and differentiation theory, Wiley and Sons, N.Y., 1988 | MR | Zbl