Semicontinuity conditions and monotonicity (Q909049)

This lengthy paper includes twelve theorems, among which Theorems 7, 8, 9 and 12 are directly devoted to the monotonicity of real functions defined on the unit interval. The rest deals with numerous classes, some of which are well known (e.g. Darboux functions, \(T_ 1\), \(T_ 2\), VB, VBG, AC, ACG, and so on) and some are introduced by the author (e.g. \(C_ i\), \(C_ d\), Darboux-). The main results are stronger than a classical theorem of Bruckner and Świątkowski.