一个可数元胞拓扑群，其所有可数子集都是闭的，不必是$\mathbb{R}$-可因数的

IF 0.2 Q4 MATHEMATICS

Commentationes Mathematicae Universitatis Carolinae Pub Date : 2023-11-13 DOI:10.14712/1213-7243.2023.016

Mikhail Tkachenko

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引用次数: 0

摘要

构造了一个Hausdorff拓扑群$G$，使得$G$是$G$的不定数(因此，$G$具有可数胞性)，$G$的所有可数子集都是闭的，$C$-嵌入在$G$中，但$G$不是$\mathbb{R}$-可因数的。这就从反面解决了《拓扑群与相关结构》(2008)一书中的8.6.3题。

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A countably cellular topological group all of whose countable subsets are closed need not be $\mathbb{R}$-factorizable

We construct a Hausdorff topological group $G$ such that $\aleph_1$ is a precalibre of $G$ (hence, $G$ has countable cellularity), all countable subsets of $G$ are closed and $C$-embedded in $G$, but $G$ is not $\mathbb{R}$-factorizable. This solves Problem 8.6.3 from the book ``Topological Groups and Related Structures" (2008) in the negative.

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来源期刊

Commentationes Mathematicae Universitatis Carolinae MATHEMATICS-

CiteScore

0.60

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0.00%

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