Topological properties of spaces of Baire functions

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Abstract

A fundamental result proved by Bourgain, Fremlin and Talagrand states that the space B1(M) of Baire one functions over a Polish space M is an angelic space. Stegall extended this result by showing that the class B1(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 Bα(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) Bα(X,G) is a κ-Fréchet–Urysohn space and hence it is an Ascoli space, and (2) Bα(X,G) is a k-space iff X is countable.

Original languageEnglish
Pages (from-to)1085-1099
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume478
Issue number2
DOIs
StatePublished - 15 Oct 2019

Keywords

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

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