The points of discontinuity of \(K_{h}C\)-functions on subsets of the product (Q2850462)

For any topological spaces \(X\) and \(Y\) and subsets \(E,B\subseteq Y\) the author considers the Choquet game \(\text{Ch}(X)\) and a game \(\text{Ma}_E(Y,B)\), which is an analogue of the Bouziad game \(\text{Bou}_{E^2}(Y^2,\Delta_B,\Delta_X)\). The following result is proved: if \(F\subseteq X\times Y\) is an upper semicontinuous compact-valued mapping such that \(F(X)\subseteq B\) and additionally one of the games \(\text{Ch}(X)\), \(\text{Ma}_E(Y, B)\) is \(\alpha\)-favourable and the other one is \(\beta\)-unfavourable, then for a metrizable space \(Z\) and a \(K_h^EC\)-function \(f:X\times Y\to Z\), the projection to \(X\) of the intersection of \(F\) and the discontinuity point set of \(f\) is meager.