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On Separately Continuous Functions of the First Baire Class on Squares and Mixed Products
Abstract
We consider Mykhaylyuk's problem asking whether the Baire-one property for every separately continuous real-valued function on each of the squares X2 and Y2 implies the same property on X× Y. Assuming b>ω1, the article obtains a negative answer using the compact cube K=[−1,1]ω1 and the space E=(c00(ω1),σ(c00(ω1),ℓ∞(ω1))). It presents a finite-coordinate characterization of Baire-one functions on E under this hypothesis.
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BibTeX
@misc{osipov2026separately,
title = {{On Separately Continuous Functions of the First Baire Class on Squares and Mixed Products}},
author = {Alexander V. Osipov},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01818},
eprint = {2611.01818},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01818},
}
RIS
TY - UNPB
TI - On Separately Continuous Functions of the First Baire Class on Squares and Mixed Products
AU - Alexander V. Osipov
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01818
UR - https://arxiv.org/abs/2611.01818
AB - We consider Mykhaylyuk's problem asking whether the Baire-one property for every separately continuous real-valued function on each of the squares X^2 and Y^2 implies the same property on X× Y. Assuming b>ω_1, the article obtains a negative answer using the compact cube K=[−1,1]^ω_1 and the space E=(c_00(ω_1),σ(c_00(ω_1),ℓ_∞(ω_1))). It presents a finite-coordinate characterization of Baire-one functions on E under this hypothesis.
ER -