Baire functions and non-isolated non-monotone discontinuities

Abstract

We show that a Baire function on a metric space can be described in terms of its restrictions on specific subsets. Furthermore, it is proved that for a real-valued function on a subset of R, among all points of discontinuity, the non-isolated non-monotone points are crucial to determining whether the function is a Baire function or not. © 2024 Elsevier B.V.