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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**Journal Articles**

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

**Last modified January 20, 2014.**