For an index set \(\Gamma \) and a cardinal number \(\kappa \) the \(\Sigma _{\kappa }\) -product of real lines \(\Sigma _{\kappa }(\mathbb {R}^{\Gamma })\) consist of all elements of \(\mathbb {R}^{\Gamma }\) with \(<\kappa \) nonzero coordinates. A compact space is \(\kappa \) -Corson if it can be embedded into \(\Sigma _{\kappa }(\mathbb {R}^{\Gamma })\) for some \(\Gamma \) . We also consider a class of compact spaces wider than the class of \(\omega \) -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 \(C_{p}(X)\) be the space of real continuous functions on the space X, endowed with the pointwise convergence topology. We present here a characterisation of \(\kappa \) -Corson compact spaces K for regular, uncountable cardinal numbers \(\kappa \) in terms of function spaces \(C_{p}(K)\) , extending a theorem of Bell and Marciszewski and a theorem of Pol. We also prove that classes of NY compact spaces and \(\omega \) -Corson compact spaces K are preserved by linear homeomorphisms of function spaces \(C_{p}(K)\) .
