Geodesic
The Hausdorff problem
Matematičeskie zametki, Tome 14 (1973) no. 2, pp. 197-200 
S. P. Ponomarev. The Hausdorff problem. Matematičeskie zametki, Tome 14 (1973) no. 2, pp. 197-200. http://geodesic.mathdoc.fr/item/MZM_1973_14_2_a3/
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     author = {S. P. Ponomarev},
     title = {The {Hausdorff} problem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {197--200},
     year = {1973},
     volume = {14},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_2_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that if the set of points of discontinuity of a real and everywhere symmetrically continuous function $f(x)$, $x\in(a,b)$, is closed, then it is not more than countable.