Under a fairly mild completeness condition on spaces Y and Z we show that every x -continuous function f : X × Y × Z → M has a “substantial” set C ( f ) of points of continuity. Some odds and ends concerning a related earlier result shown by the authors are presented. Further, a generalization of S . Kempisty's ideas of generalized continuity on products of finitely many spaces is offered. As a corollary from the above results, a partial answer to M . Talagrand's problem is provided.