Digging into the classes of κ-Corson compact spaces

Abstract For any cardinal number κ and an index set Γ, the Σ κ -product of real lines Σ κ (ℝ Γ ) consists of all elements of ℝ Γ having < κ many nonzero coordinates. A compact space K is κ -Corson compact if it can be embedded into Σ κ (ℝ Γ ) for some Γ. The class of ( ω 1 )-Corson compact spaces has been intensively studied over the last decades. We discuss properties of κ -Corson compacta for various cardinal numbers κ as well as properties of related Boolean algebras and spaces of continuous functions. We present here a detailed discussion of the class of ω -Corson compacta extending the results of Nakhmanson and Yakovlev [NY]. For κ > ω , our results on κ -Corson compact spaces are related to the line of research originated by Kalenda [Ka2] and Bell and Marciszewski [BM], and continued by Bonnet, Kubiś and Todorčević in their recent paper [BKT].