Abstract
We investigate the problem of the dependence of separately continuous functions on n coordinates on products of spaces each of which is a topological product. In the case where X and Y are products of completely regular countably compact spaces, we establish necessary and sufficient conditions for such a dependence.
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References
V. K. Maslyuchenko and V. V. Mikhailyuk, “Separately continuous functions on products of compact sets and their dependence on n variables,” Ukr. Mat. Zh., 47, No. 3, 344–350 (1995).
R. Engelking, General Topology [Russian translation], Mir, Moscow (1986).
N. Noble and M. Ulmer, “Factoring functions on Cartesian products,” Trans. Amer. Math. Soc., 163, 329–339 (1972).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 6, pp. 822–829, June, 1998.
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Mikhailyuk, V.V. Dependence of separately continuous functions on n coordinates on products of compact sets. Ukr Math J 50, 934–943 (1998). https://doi.org/10.1007/BF02515227
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DOI: https://doi.org/10.1007/BF02515227