×

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.

MSC:

26A21 Classification of real functions; Baire classification of sets and functions
PDFBibTeX XMLCite
Full Text: arXiv