Finite Decompositions for Initial Baire-1 Subclasses and Their Characterization via Homogeneous Sequences

We announce some results concerning initial subclasses of the Baire-1 functions. First, we obtain a finite decomposition into continuous maps for a basic initial subclass. Second, we give a pointwise description of initial subclasses via point-homogeneous sequences. Third, we present a finite decomposition of maps into open and closed maps.