This article shows that for completely regular spaces X1, ..., Xn with xi0 – a non-isolated Gδ-point in the space Xi
, if for some 1 ≤ i ̸= j ≤ n there exists a differently continuous function g : Xi × Xj → R, then there exists a differently continuous function f :
∏n
i=1
Xi → R
such that D(f) = {(x10, ..., xn0)}. Using this fact, the main result is shown, that for completely regular spaces X1, ..., Xn, the existence of a differently continuous function f : ∏n i=1 Xi → R with a single-point discontinuity (x10, ..., xn0), where xi0 is a Gδ point in Xi, is equivalent to the fact that out of n P-filters at least two are almost coherent.

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