Decomposing symmetrically continuous and Sierpinski-Zygmund functions into continuous functions

In this paper we will investigate the smallest cardinal number such that for any symmetrically continuous function there is a partition of such that every restriction is continuous. The similar numbers for the classes of Sierpinski-Zygmund functions and all functions from to are also investigated and it is proved that all these numbers are equal. We also show that and that it is consistent with ZFC that each of these inequalities is strict.