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arXiv · 2507.14889

There are No Product and Subgroup Theorems for the Covering Dimension of Topological Groups

Ol'ga Sipacheva
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Abstract

Strongly zero-dimensional topological groups $G_1$, $G_2$, and $G$ such that $G_1\times G_2$ has positive covering dimension and $G$ contains a closed subgroup of positive covering dimension are constructed. Moreover, all finite powers of $G_1$ are Lindel\"of and $G_2$ is second-countable. An example of a strongly zero-dimensional space $X$ whose free, free Abelian, and free Boolean topological groups have positive covering dimension is also given.

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Ol'ga Sipacheva. 2025-07-20. There are No Product and Subgroup Theorems for the Covering Dimension of Topological Groups. https://arxiv.org/abs/2507.14889

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