Compact spaces of separately continuous functions in two variables

For compacta X and Y, let SCp(X×Y) be the space of all separately continuous functions on the product X×Y with the topology of pointwise convergence. We prove that any compact subspace Z in SCp(X×Y) is a Corson compactum in the case where X or Y is ccc (= has the Souslin property). We study this new class of compacta.