arXiv Open Access 2025

The $Δ_1$-property of $X$ is equivalent to the Choquet property of $B_1(X)$

Alexander V. Osipov

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Abstrak

We give a characterization of the $Δ_1$-property of any Tychonoff space $X$ in terms of the function space $B_1(X)$ of all Baire-one real-valued functions on a space $X$ with the topology of pointwise convergence. We establish that for a Tychonoff space $X$ the $Δ_1$-property is equivalent to the Choquet property of $B_1(X)$. Also we construct under $ZFC$ an example of a separable pseudocompact space $X$ such that $C_p(X)$ is $κ$-Frechet-Urysohn but $X$ fails to be a $Δ_1$-space. This answers a question of Kakol-Leiderman-Tkachuk.

Topik & Kata Kunci

math.GN

Penulis (1)

Alexander V. Osipov

Format Sitasi

APA MLA BibTeX

Osipov, A.V. (2025). The $Δ_1$-property of $X$ is equivalent to the Choquet property of $B_1(X)$. https://arxiv.org/abs/2503.10491

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓