On composition of Baire functions

Abstract

We study the maps between topological spaces whose composition with Baire class α maps also belongs to the α'th Baire class and give characterizations of such maps.

A generalization of a Baire theorem concerning barely continuous functions

“…Let us observe that a similar result for Y = R was obtained by Mykhaylyuk [14]. The next theorem was recently proved in [10,Theorem 10].…”

A survey on composition operators on some function spaces

“…The following result follows from Theorem 3 of [17], in the case of Baire one functions and, more generally, from Theorem D of [20], for Baire functions of class n. We have that, in the case of Baire functions, the composition operator behaves well. Namely, the following holds.…”

Extending Baire-one functions on compact spaces

“…Baire-one in the case either dimX = 0, or Y is a metric contractible locally path-connected space [11,12].…”