Topological properties of spaces of Baire functions

2019/04/27 by Gabriyelyan, Saak · 3 citations
#46A03 #46A08 #54C35 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1904.13227

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 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.

Cited by

• New classes of compact-type spaces
• κ-spaces
• On k_ℝ-spaces and s_ℝ-spaces

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