## Abstract

A fundamental result proved by Bourgain, Fremlin and Talagrand states that the space B_{1}(M) of Baire one functions over a Polish space M is an angelic space. Stegall extended this result by showing that the class B_{1}(M,E) of Baire one functions valued in a normed space E is angelic. These results motivate our study of various topological properties in the classes B_{α}(X,G) of Baire-α functions, where α is a nonzero countable ordinal, G is a metrizable non-precompact abelian group and X is a G-Tychonoff first countable space. In particular, we show that (1) B_{α}(X,G) is a κ-Fréchet–Urysohn space and hence it is an Ascoli space, and (2) B_{α}(X,G) is a k-space iff X is countable.

Original language | English |
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Pages (from-to) | 1085-1099 |

Number of pages | 15 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 478 |

Issue number | 2 |

DOIs | |

State | Published - 15 Oct 2019 |

## Keywords

- Ascoli
- Baire functions
- Normal space
- k-Space
- κ-Fréchet–Urysohn