Characterization of the sets of discontinuity points of separately continuous functions of many variables on the products of metrizable spaces

We show that a subset of the product ofn metrizable spaces is the set of discontinuity points of some separately continuous function if and only if this subset can be represented in the form of the union of a sequence ofF _σ-sets each, of which is locally projectively a set of the first category. Chernovsty University, Chernovtsy. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp. 740–747, June, 2000.