PreprintCC BY-NC-ND 4.0arXiv
Baire 1 functions and the strong Choquet property
Abstract
Let X be a Tychonoff space and B_1(X) be the space of real-valued Baire 1 functions. Using the classical Lebesgue's characterization of Baire 1 functions and the strong Choquet game we prove that if X is locally compact or a topological sum of sigma-compact spaces, the space B_1(X) equipped with the topology τ_UC of uniform convergence on compacta, is a strong Choquet space. For the Sorgenfrey line S, the space (B_1(S); τ_UC) is of the first Baire category in itself.
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BibTeX
@misc{hola2026baire,
title = {{Baire 1 functions and the strong Choquet property}},
author = {Ľubica Holá},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34517},
eprint = {2609.34517},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34517},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Baire 1 functions and the strong Choquet property
AU - Ľubica Holá
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34517
UR - https://arxiv.org/abs/2609.34517
AB - Let X be a Tychonoff space and B_1(X) be the space of real-valued Baire 1 functions. Using the classical Lebesgue's characterization of Baire 1 functions and the strong Choquet game we prove that if X is locally compact or a topological sum of sigma-compact spaces, the space B_1(X) equipped with the topology τ_UC of uniform convergence on compacta, is a strong Choquet space. For the Sorgenfrey line S, the space (B_1(S); τ_UC) is of the first Baire category in itself.
ER -