Separately continuous functions on products of locally convex spaces with the weak topology

We study the inverse problem of the theory of separately continuous functions, that is, the problem of constructing a separately continuous function with a prescribed set of points of discontinuity. It is shown that for a given F-set C in the product X×Y of two spaces X and Y in the class of compatible spaces, which includes in particular metrizable spaces and semireflexive locally convex spaces in the weak topology with a metrizable separable dual embedded in the product A×B of the sets AX and BY of first category in X and Y respectively, there exists a separately continuous function f. X×Y whose set of points of discontinuity is C.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 3, 1997, pp. 25–30.