Inverse problems of the theory of separate-continuous images - Maslyuchenko, V. K.; Mikhailyuk, V. V.; Sobchuk, О. V. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
The present paper investigates the problem of constructing a separately continuous function defined on the product of two topological spaces that possesses a specified set of points of discontinuity and the related special problem of constructing a pointwise convergent sequence of continuous functions that possesses a specified set of points of nonuniform convergence and set of points of discontinuity of a limit function. In the metrizable case the former problem is solved for separable $F_σ$-sets whose projections onto every cofactor is of the first category. The second problem is solved for a pair of embedded $F_σ$.