Linearly ordered families of Baire 1 functions. (English) Zbl 1014.26010

The author considers the set of Baire 1 functions endowed with the pointwise partial ordering and investigates the structure of linearly ordered subsets. By a theorem of Kuratowski \(\omega _1\) is not representable by real Baire 1 functions. The main goal of this paper is to present some constructions of representable ordered sets which show that Kuratowski’s theorem is not too far from being characterization.


26A21 Classification of real functions; Baire classification of sets and functions
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