Another note on Kempisty's generalized continuity
In the fundamental theorem the authors show that, under some assumptions on the spaces X, Y, Z and M, for any x-continuous function f: \(X\times Y\times Z\to M\), the set of all continuity points of f is a dense \(G_{\delta}\) subset in \(\{\) \(x\}\) \(\times X\times Z\) for each \(x\in X\). Some examples connected with x-continuity and quasi-continuity are also included. The authors give a partial solution to a problem of M. Talagrand.
scientific article; zbMATH DE number 4103944