Rosenthal compacta and lexicographic products

For a metrizable space X, by B_1(X) we denote the space of real valued functions of the first Baire class on X, endowed with pointwise convergence topology. A compact space K is called Rosenthal compact if it can be embedded in B_1(X) for some completely metrizable separable space X. We consider two subclasses of the class R of Rosenthal compacta - RK (we additionally require that the space X is compact) and CD (here, we consider compact spaces which can be represented as spaces of functions on X with countably many discontinuities), where CD is a subclass of RK. It was proven by Pol, that classes RK and R are different, by giving appropriate example. Later another example was given by W. Marciszewski and Pol. Finally, Antonio Aviles and Stevo Todorcevic gave two examples of spaces from RK\CD.

The talk is based on the paper by A. Aviles and S. Todorcevic, Lexicographic products as compact spaces of the first Baire class, Topology Appl. 267 (2019), 106871.