In this paper we will investigate the smallest cardinal number \kappa such that for any symmetrically continuous function f:R-->R there is a partition {X_\xi:\xi<\kappa} of R such that every restriction f|X_\xi: X_\xi-->R is continuous. The similar numbers for the classes of Sierpinski-Zygmund functions and all functions from R to R are also investigated and it is proved that all these numbers are equal. We also show that \kappa is between cf(c) and c and that it is consistent with ZFC that \kappa=cf(c)<c and that cf(c)<c=\kappa.

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K. Ciesielski, Set Theoretic Real Analysis, J. Appl. Anal. 3(2) (1997), 143-190. MR 99k:03038

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