We call a spaces $X$ equicompact if a closure of any relatively pseudocompact subset of $X$ is compact. Denote by $SC_p(X,Y)$  a space of all separately continuous mappings $f: X =  \prod_{i=1}^d X_i → Y$ with the poinwise convergent topology. Let $X$ be the product of countable Cech complete spaces $X_1, ..., X_d$ and $Y$ be a metrizable space. We prove that $SC_p(X,Y)$ is equicompact. We also prove that for each $T_1$-space $X$ there exists an equicompact $T_1$- space $μX ⊇ X$ such that ${\overline X} = μX$ and any continuous mapping from $X$ to an completely regular equicompact space $Y$ admits a continuous extention on $μX$.

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