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There are $ 2\sp c$ symmetrically continuous functions


Author: Miroslav Chlebík
Journal: Proc. Amer. Math. Soc. 113 (1991), 683-688
MSC: Primary 26A15; Secondary 26A21
MathSciNet review: 1069685
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Abstract: The purpose of this paper is to prove that the power of the set of symmetrically continuous real functions is $ {2^c}$ ($ c$ is the power of the continuum). This surprisingly contrasts with the set of continuous (or Borel) real functions, the power of which is $ c$.


References [Enhancements On Off] (What's this?)

  • [1] N. K. Bari, Trigonometrical series, Moscow, 1961. (Russian)
  • [2] M. J. Evans and L. Larson, The continuity of symmetric and smooth functions, Acta Math. Hungar. 43 (1984), no. 3-4, 251–257. MR 733857, 10.1007/BF01958022
  • [3] H. Fried, Über die symmetrische Stetigkeit von Funktionen, Fund. Math. 29 (1937), 134-137.
  • [4] F. Hausdorff, Problem #62, Fund. Math. 25 (1935), 578.
  • [5] Lee Larson, Symmetric real analysis: a survey, Real Anal. Exchange 9 (1983/84), no. 1, 154–178. MR 742782
  • [6] -, Query #170, Real Anal. Exchange 4 (1983-84), 29.
  • [7] David Preiss, A note on symmetrically continuous functions, Časopis Pěst. Mat. 96 (1971), 262–264, 300 (English, with Czech summary). MR 0306411

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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1069685-8
Article copyright: © Copyright 1991 American Mathematical Society