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Some function applications of weak λ-spaces
Abstract
In this paper it is proved that there exists (in ZFC) a separable pseudocompact weak λ-space X which is not Δ1-space. It follows that there exists a space X such that B1(X,[0, 1]) is Choquet, while B1(X) is not Choquet. Also it is proved that there exists a γ-set X which is not weak λ-set. It follows that there exists a zero-dimensional separable metrizable space X such that B1(X) is Baire, while B1(X, [0,1]) is not Choquet. These results answers the previously posed questions.
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BibTeX
@misc{osipov2026some,
title = {{Some function applications of weak $λ$-spaces}},
author = {Alexander V. Osipov},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30278},
eprint = {2608.30278},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30278},
}
RIS
TY - UNPB
TI - Some function applications of weak λ-spaces
AU - Alexander V. Osipov
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30278
UR - https://arxiv.org/abs/2608.30278
AB - In this paper it is proved that there exists (in ZFC) a separable pseudocompact weak λ-space X which is not Δ_1-space. It follows that there exists a space X such that B_1(X,[0, 1]) is Choquet, while B_1(X) is not Choquet. Also it is proved that there exists a γ-set X which is not weak λ-set. It follows that there exists a zero-dimensional separable metrizable space X such that B_1(X) is Baire, while B_1(X, [0,1]) is not Choquet. These results answers the previously posed questions.
ER -