Geodesic
Classification of spaces of Baire functions on ordinal intervals
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 3, pp. 61-66
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A complete linear homeomorphic classification of the spaces $B_p[1,\alpha]$ of all Baire functions $f\colon[1,\alpha]\to\mathbb R$ that are defined on ordinal intervals $[1,\alpha]$ and are equipped with the topology of pointwise convergence is given. Since any Baire function on an ordinal interval belongs to the first Baire class, our classification is also a classification of spaces of functions of the first Baire class. A similar classification is given for spaces of two-valued Baire functions $f\colon[1,\alpha]\to\{0,1\}$.
Keywords: spaces of Baire functions, ordinals, topology of pointwise convergence, linear homeomorphisms
Mots-clés : classification. 
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L. V. Genze; S. P. Gul'ko; T. E. Khmyleva. Classification of spaces of Baire functions on ordinal intervals. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 3, pp. 61-66. http://geodesic.mathdoc.fr/item/TIMM_2010_16_3_a4/

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