Abstract
By using the theorem on the density of the topological product and the generalized theorem on the dependence of a continuous function defined on a product of spaces on countably many coordinates, we show that every separately continuous function defined on a product of two spaces representable as products of compact spaces with density ≤\(\mathfrak{n}\) depends on\(\mathfrak{n}\) variables. In the case of metrizable compact sets, we obtain a complete description of the sets of discontinuity points for functions of this sort.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 344–350, March, 1995.
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Maslyuchenko, V.K., Mikhailyuk, V.V. Separately continuous functions on products of compact sets and their dependence on\(\mathfrak{n}\) variables. Ukr Math J 47, 401–407 (1995). https://doi.org/10.1007/BF01056302
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DOI: https://doi.org/10.1007/BF01056302