Some remarks on Baire’s grand theorem

Games characterizing certain families of functions

“…In the recent decades, several nice characterizations for some classes of regular functions were obtained. Duparc [7] and Carroy [6] characterized Baire 1 functions from N N into itself by using the so-called eraser game (for more applications of this game, see [4]). Other significant results for different classes of functions between Polish zero-dimensional Polish spaces are due to Andretta [2] (a game characterization of ∆ ∆ ∆ 0 2 -measurable functions), Semmes [18] (Borel functions), Nobrega [16] (Baire class ξ functions) and Ros [17] (piecewise defined functions).…”