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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1069685-8
PII: S 0002-9939(1991)1069685-8
Article copyright: © Copyright 1991 American Mathematical Society