Using ideas and results from recursion theory and effective descriptive set theory we provide a partial answer to the Decomposabilty Conjecture in Polish spaces of small inductive dimension. The latter extends earlier work of Motto Ros and Pawlikowski-Sabok. We also state a conjecture, which would allow our arguments to be carried out in all Polish spaces, and we give the analogous results in the transfinite case of the problem. Finally we present an approach to the later, where we utilize the technique of turning Borel-measurable functions into continuous ones.