Associated sets and continuity roads (Q1062154)

For a real-valued function f the associated sets of f are the sets \(\{x: f(x)>a\}\) and \(\{x: f(x)<a\}\) for \(a\in R\). For a function of one real variable the continuity road for f at a point x in its domain is a set E containing x such that the restriction of f to the domain E is continuous at x. Some classes of functions are defined or characterized in terms of their associated sets or in terms of continuity roads. The author obtains general results relating to the two types of characterization of functions belonging to subclasses of Baire class one. This method makes it possible to replace a characterization of one type for the other. He adopts the method to the Zahorski classes with the exception of the class \({\mathcal M}_ 4\).