Abstract
We provide a game theoretical proof of the fact that if f is a function from a zero-dimensional Polish space to \( \mathbb N^{\mathbb N}\) that has a point of continuity when restricted to any non-empty compact subset, then f is of Baire class 1. We use this property of the restrictions to compact sets to give a generalisation of Baire’s grand theorem for functions of any Baire class.
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Camerlo, R., Duparc, J. Some remarks on Baire’s grand theorem. Arch. Math. Logic 57, 195–201 (2018). https://doi.org/10.1007/s00153-017-0563-6
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DOI: https://doi.org/10.1007/s00153-017-0563-6