We prove the following result. Let $X_1,...,X_n,T$ be topological spaces with $X_2,...,X_n$ first countable and $T$ second countable. If $f : X_1 × ... × X_n → Z$  is a separately continuous mapping, where $Z$ is the space of all continuous functions $z : T → \mathbb{R}$  with the topology of either pointwise convergence $C_p(T)$ or compact-open topology $C_k(T),$ then the continuity point set $C(f)$  is residual in the product $X_1 × ... × X_n$.

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