A category base for Mycielski's ideals (Q1322615)

On the base of playing a certain game (choosing sequences that belong or do not belong to some subset of the Cantor space \(C\)), the author defines a category base on \(C\) in the sense of \textit{J. C. Morgan} [Fundam. Math. 94, 13-23 (1977; Zbl 0371.54014)]. No element of the defined category base is meager; the Mycielski ideal on \(C\) with respect to a given game coincides with meager sets determining the game.