Одержано новi узагальнення теореми Серпiнського про однозначну визначенiсть нарiзно неперервної функцiї на добутку своїми значеннями на довiльнiй всюди щiльнiй множинi.

[1] Comfort W.W. Functions linearly continuous on a product of Baire spaces Boll. Un. Mat. Ital. 20 (1965), 128–134.
[2] Engelking R., General Topology, Revised and completed edition, Heldermann Verlag, Berlin (1989).
[3] Goffman C., Neugebauer C.J. Linearly continuous functions Proc. Amer. Math. Soc. 12 (1961), 997–998.
[4] Henriksen M., Woods R. G. Separate versus joint continuity: A tale of four topologies, Top. Appl. 97 (1999), 175–205.
[5] Marcus S. On functions continuous in each variable, Doklady Akad. Nauk SSSR. 112 (1957), 812–814.
[6] Maslyuchenko V.К, Filipchuk О.I. New generalizations of Serpinsky’s theorem, Math. studiyi 47 (1) (2017), 91–99.
[7] Mykhaylyuk V.V. Separate continuity topology and a generalization of Sierpinski’s theorem, Math. Stud. 14 (2) (2000), 193–196.
[8] Mykhaylyuk V. Namioka spaces, GO-spaces and o-game, Top. Appl. 235 (2018), 1–13.
[9] Mykhaylyuk V., Pol R. On a problem of Talagrand concerning separately continuous functions, Journal of the Institute of Mathematics of Jussieu (accepted).
[10] Namioka I. Separate contimuity and joint continuity, Pacif. J. Math. 51 (2) (1974), 515–531.
[11] Piotrowski Z., Wingler E.Y. On Sierpinski’s theorem on the determination of separately continuous functions, Q&A in General Topology. 15 (1997), 15–19.
[12] Sierpinski W. Sur une propertie de fonctions de deux variables reeles, continues par rapport a chacune de variables, Publ. Math. Univ. Belgrade. 1 (1932), 125–128.
[13] Tolstov G. On partial derivatives, Amer. Math. Soc. (transl. 69), Izv. Akad. Nauk SSSR Mat. 13 (1949), 425–449.