Function spaces on Corson-like compacta

For an index set Γ and a cardinal number κ the Σκ-product of real lines Σκ(RΓ) consist of all elements of RΓ with <κ nonzero coordinates. A compact space is κ-Corson if it can be embedded into Σκ(RΓ) for some Γ. We also consider a class of compact spaces wider than the class of ω-Corson compact spaces, investigated by Nakhmanson and Yakovlev as well as Marciszewski, Plebanek and Zakrzewski called $NY$ compact spaces. For a Tychonoff space X, let Cₚ(X) be the space of real continuous functions on the space X, endowed with the pointwise convergence topology. We present here a characterisation of κ-Corson compact spaces K for regular, uncountable cardinal numbers κ in terms of function spaces Cₚ(K), extending a theorem of Bell and Marciszewski and a theorem of Pol. We also prove that classes of $NY$ compact spaces and ω-Corson compact spaces K are preserved by linear homeomorphisms of function spaces Cₚ(K).