On the ideal convergence of sequences of Świątkowski functions

For any Borel ideal \(\mathscr {I}\) the class of \(\mathscr {I}\)-limits of sequences of Świątkowski functions is described. In particular, we characterize Borel ideals \(\mathscr {I}\) for which classes of ideal and ordinary limits of sequences of Świątkowski functions coincide. We consider also ideal limits of sequences of functions possessing the Świątkowski property related to some density-type topologies. Moreover, an alternative characterization of ordinary limits of sequences of Świątkowski functions is given.