A complete topological classification of the space of Baire functions on ordinals (Q1731390)

Let $\alpha$ and $\beta$ be infinite ordinals. Let $B_{p}[1,\alpha]$ be the space of all Baire functions from the ordinal segment $[1,\alpha]$ into $\mathbb{R}$ equipped with the topology of pointwise convergence. In this paper, the authors prove that the spaces $B_{p}[1,\alpha]$ and $B_{p}[1,\beta]$ are homeomorphic if and only if they are linearly homeomorphic. Linear topological classification of these spaces was given by the same authors in [``Classification of spaces of Baire functions on ordinal intervals'', Trudy Inst. Mat. i Mekh. Uro RAN 16, No. 3, 61--66 (2010)].