Abstract
It is proved that if the set of points of discontinuity of a real and everywhere symmetrically continuous functionf(x), x ∈ (a, b), is closed, then it is not more than countable.
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F. Hausdorff, Problème No. 62, Fund. Math.,25, 578 (1935).
H. Fried, “Über die symmetrische Stetigkeit von Funktionen,” Fund. Math.,29, 134–137 (1937).
I. N. Pesin, “The measurability of symmetrically continuous functions,” Doklady i Soobshcheniya, L'vovskii Gosuniversitet, 9 (II) (1961).
W. Sierpinskii, “Sur une fonction non mesurable partout presque symmétrique,” Acta Scient. Math. Szeged,8, 1–6 (1936).
Z. Charzynski, “Sur les fonctions dont la dérivée symmétrique est partout finie,” Fund. Math.,21, 214–216 (1933).
S. Marcus, “Sur un problème de F. Hausdorff concernant les fonctions symmétriques continues,” Bulletin de l'Académie Polonaise des Sciences,4, No. 4, 201–205 (1956).
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Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 197–200, August, 1973.
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Ponomarev, S.P. The Hausdorff problem. Mathematical Notes of the Academy of Sciences of the USSR 14, 671–672 (1973). https://doi.org/10.1007/BF01147111
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DOI: https://doi.org/10.1007/BF01147111