Function spaces on Corson-like compacta

Recall that a compact space is Eberlein compact if it is homeomorphic to a subspace of some Banach space equipped with the weak topology. A compact space is \omega-Corson compact if it embeds into a \sigma-product of real lines, that is a subspace of the product R^{\Gamma} consisting of sequences with finitely many nonzero coordinates for some set \Gamma. Every \omega-Corson compact space is Eberlein compact. For a Tichonoff space X, let Cp(X) denote the space of real continuous functions on X endowed with the pointwise convergence topology. During the talk we will show that the class \omega-Corson compact spaces K is invariant under linear homeomorphism of function spaces Cp(K) and other related results.