In mathematics, Baire functions are functions obtained from continuous functions by transfinite iteration of the operation of forming pointwise limits of sequences of functions. They were introduced by René-Louis Baire in 1899. A Baire set is a set whose characteristic function is a Baire function. == Classification of Baire functions == Baire functions of class α, for any countable ordinal number α, form a vector space of real-valued functions defined on a topological space, as follows. The Baire class 0 functions are the continuous functions. The Baire class 1 functions are those functions which...