Three topological reducibilities for discontinuous functions
Three topological reducibilities for discontinuous functions
We define a family of three related reducibilities, $\leq _{\mathbf {T}}$, $\leq _{\mathbf {tt}}$ and $\leq _{\mathbf {m}}$, for arbitrary functions $f,g:X\rightarrow \mathbb R$, where $X$ is a compact separable metric space. The $\equiv _{\mathbf T}$-equivalence classes mostly coincide with the proper Baire classes. We show that certain $\alpha$-jump functions …