Geodesic
Most Infinitely Differentiable Functions are Nowhere Analytic
Canadian mathematical bulletin, Tome 16 (1973) no. 4, pp. 597-598

Voir la notice de l'article provenant de la source Cambridge University Press

We define a natural metric, d, on the space, C∞, , of infinitely differentiable real valued functions defined on an open subset U of the real numbers, R, and show that C∞, is complete with respect to this metric. Then we show that the elements of C∞, which are analytic near at least one point of U comprise a first category subset of C∞, . 
Darst, R. B. Most Infinitely Differentiable Functions are Nowhere Analytic. Canadian mathematical bulletin, Tome 16 (1973) no. 4, pp. 597-598. doi: 10.4153/CMB-1973-098-3
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