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arXiv · 2610.08206

Lindelöf-type properties of spaces of Baire-one functions

Alexander V. Osipov·Evgenii Reznichenko
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Abstract

In this paper, we investigate Lindelöf-type properties of spaces of Baire-one functions equipped with the topology of pointwise convergence. In particular, we investigate the properties of normality, extent and realcompactness for the space $B_1(X)$ of Baire-one real-valued functions. We also study when $B_1(X)$ is realcompact: we show that this is the case for every hereditarily Baire (in particular, every Polish) separable metrizable space $X$ and for every Luzin set $X$. The paper provides answers to two Teng's questions. The paper raises open questions.

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BibTeXRIS

Alexander V. Osipov, Evgenii Reznichenko. 2026-10-06. Lindelöf-type properties of spaces of Baire-one functions. https://arxiv.org/abs/2610.08206

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