Lindelöf-type properties of spaces of Baire-one functions
Alexander V. Osipov, Evgenii Reznichenko
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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