  Let $X$ and $Y$ be pseudocompact spaces and let the function $\Phi: X\times
Y\to \mathbb R$ be separately continuous. The following conditions are
equivalent: (1) there is a dense $G_\delta$ subset of $D\subset Y$ so that
$\Phi$ is continuous at every point of $X\times D$ (Namioka property); (2)
$\Phi$ is quasicontinuous; (3) $\Phi$ extends to a separately continuous
function on $\beta X\times \beta Y$. This theorem makes it possible to combine
studies of the Namioka property and generalizations of the
Eberlein-Grothendieck theorem on the precompactness of subsets of function
spaces. We also obtain a characterization of separately continuous functions on
the product of several pseudocompact spaces extending to separately continuous
functions on products of Stone-Cech extensions of spaces. These results are
used to study groups and Mal'tsev spaces with separately continuous operations.
