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A Baire space $B$ and a compact space $K$ satisfy the Namioka property $N(B,K)$ if for every separately continuous function $f: B\times K\to R$ there is a dense set $A\subset B$ such that $f$ is jointly continuous at each poin of $A\times K$. Its proved that $N(B,K)$ and $N(B,L)$ imply $N(B,K\times L$. It follows in particular that the class of co-Namioka compact spaces is stable under (arbitrary) product.

The class of co-Namioka compact spaces is stable under product