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Solution of the Baire order problem of Mauldin. (English) Zbl 0847.26005

Let \(C_I\) be the family of all real functions defined on an uncountable separable and complete metric space whose sets of discontinuity points belong to a uniform \(\sigma\)-ideal \(I\). It is proved that the Baire order of \(C_I\) is \(= 1\) or \(\omega_1\).

MSC:

26A21 Classification of real functions; Baire classification of sets and functions
03E15 Descriptive set theory
54C30 Real-valued functions in general topology
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References:

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