Every countable compact subset of $\mathbb{S}^n$ is tame

Agelos Georgakopoulos

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arXiv · 2208.11534

Every countable compact subset of $\mathbb{S}^n$ is tame

Agelos Georgakopoulos

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Abstract

We prove that any two countable, compact, subsets of $\mathbb{S}^n, n\geq 2$ that are homeomorphic also have homeomorphic complements. Thus any wild subspace like the classical construction of Antoine must contain a Cantor set.

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BibTeX RIS

Agelos Georgakopoulos. 2022-08-24. Every countable compact subset of $\mathbb{S}^n$ is tame. https://arxiv.org/abs/2208.11534

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