Work

Lindelöf-type properties of spaces of Baire-one functions

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.08206

Authors: Osipov, Alexander V., Reznichenko, Evgenii

Institutions: Ural Federal University, N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Lomonosov Moscow State University

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7220898948

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