Function spaces on Corson-like compacta

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