Descriptive aspects of Rosenthal compacta (Q2874859)

A compact space is said to be Rosenthal if it can be represented as a space of functions of the first Baire class on some Polish space equipped with the topology of pointwise convergence. The paper reports on purely topological properties of Rosenthal compacta with particular aspects in descriptive set theory. Although the full understanding of the results reviewed in the paper requires a knowledge of forcing, infinite Ramsey theory, and effective descriptive set theory the exposition of the paper is accessible for a reader with a classical standard background. In particular the following topics concerning Rosenthal compacta are discussed in the paper: the Fréchet-Urysohn property, the set of \(G_\delta\)-points, regularity properties of separable Rosenthal compacta, codings of separable Rosenthal compacta by an analytic set, spaces of continuous functions on separable Rosenthal compacta, etc.NEWLINENEWLINEFor the entire collection see [Zbl 1282.54001].