On a classification of pointwise compact sets of the first Baire class functions. (English) Zbl 0719.54022

Author’s abstract: “The paper is concerned with compact separable subspaces of the space \(B_ 1(\omega^{\omega})\) of the first Baire class functions on irrationals endowed with the pointwise topology, i.e. Rosenthal compacta. We associate to each separable Rosenthal compactum K an ordinal number \(\eta (K)\leq \omega_ 1\), which indicates the “Borel complexity” of the compactum. The index \(\eta\) (K) is a topological invariant of the function space \(C_ p(K)\) of real-valued continuous functions on K endowed with the pointwise topology. We construct Rosenthal compacta of arbitrarily large countable index and we use them to give examples of open linear continuous maps raising the Borel class of linear spaces.”


54C50 Topology of special sets defined by functions
54E52 Baire category, Baire spaces
54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
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