Separately Continuous Functions on Products and Their Dependence on ℵ Coordinates

We investigate necessary and sufficient conditions on topological products X = ∏_{s ∈ s} X _s and Y = ∏_{t ∈ T} Y _t for every separately continuous function f: X × Y → ℝ to be dependent on at most ℵ coordinates with respect to a certain coordinate.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1357 – 1368, October, 2004.