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Lindelöf-type properties of spaces of Baire-one functions
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 B1(X) of Baire-one real-valued functions. We also study when B1(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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BibTeX
@misc{osipov2026lindelöftype,
title = {{Lindelöf-type properties of spaces of Baire-one functions}},
author = {Alexander V. Osipov and Evgenii Reznichenko},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08206},
eprint = {2610.08206},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08206},
}
RIS
TY - UNPB
TI - Lindelöf-type properties of spaces of Baire-one functions
AU - Alexander V. Osipov
AU - Evgenii Reznichenko
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08206
UR - https://arxiv.org/abs/2610.08206
AB - 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.
ER -