发表机构
Krasovskii Institute of Mathematics and Mechanics, Ural Federal University（克拉索夫斯基数学力学研究所，乌拉尔联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在ZFC下构造了多个拓扑空间实例，解决了关于B₁空间的Choquet性质及贝尔性质的相关问题。
AI 中文摘要
本文在ZFC公理系统中证明，存在可分伪紧弱λ-空间X，它不是Δ₁-空间。由此可得，存在空间X使得B₁(X,[0,1])是Choquet空间，而B₁(X)不是Choquet空间。同时证明存在γ-集X，它不是弱λ-集，由此可得存在零维可分可度量化空间X，使得B₁(X)是贝尔空间，而B₁(X,[0,1])不是Choquet空间。这些结果回答了此前提出的若干问题。
英文摘要
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.
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