Abstract:
Considering the spaces $B_p[1,\alpha]$ of all Baire functions $x\colon[1,\alpha]\to\mathbb R$ on the ordinal segments $[1,\alpha]$ that are endowed with the topology of pointwise convergence, we give a complete topological classification of these spaces.
Keywords:Baire $1$-function, space of Baire functions, topology of pointwise convergence, homeomorphism, ordinal segment, order topology, real compactness.