2019
Том 71
№ 11

All Issues

Inverse problems of the theory of separately continuous mappings

Maslyuchenko V. K., Mykhailyuk V. V., Sobchuk V. S.

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Abstract

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 $F_σ$.

English version (Springer): Ukrainian Mathematical Journal 44 (1992), no. 9, pp 1108-1116.

Citation Example: Maslyuchenko V. K., Mykhailyuk V. V., Sobchuk V. S. Inverse problems of the theory of separately continuous mappings // Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1209–1220.

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