Separately continuous functions on products of compact sets and their dependence on\(\mathfrak{n}\) variables
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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.
Keywords
Continuous Function Compact Space Generalize Theorem Discontinuity Point Topological Product
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© Plenum Publishing Corporation 1996