发表机构
Institute of Mathematics, Czech Academy of Sciences; Faculty of Mathematics and Physics, Charles University（捷克科学院数学研究所; 查理大学数学与物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
构造实数线上一类非微观 $G_\delta$ 集，其所有紧致子集均为微观，解决 Zindulka 与 Nowakowski 的公开问题，方法为 Cantor 空间中编码树分支与标记节点后经二进制映射转移。
AI 中文摘要
我们构造了实数线上的一个非微观的 $G_\delta$ 子集，其所有紧致子集均为微观集，回答了 Zindulka 和 Nowakowski 提出的一个问题。我们首先在标准 Cantor 空间中通过编码有限分支树的枝以及合适标记节点的选择来获得这样的集合。对枝的编码确保所得集合不是微观的，而标记节点使我们能够构造覆盖，证明每个紧致子集都是微观的。随后，该例子通过二进制展开映射从 Cantor 空间转移到实数线。
英文摘要
We construct a nonmicroscopic $G_δ$ subset of the real line all of whose compact subsets are microscopic, answering a question of Zindulka and Nowakowski. We first obtain such a set in the standard Cantor space by coding branches of a finitely branching tree together with suitable choices of marked nodes. The coding of the branches ensures that the resulting set is not microscopic, while the marked nodes allow us to construct covers showing that every compact subset is microscopic. The example is then transferred from the Cantor space to the real line by the binary-expansion map.
Comments14 pages
