Every countable compact subset of $\mathbb{S}^n$ is tame
Geometric Topology
2022-08-25 v1 General Topology
Abstract
We prove that any two countable, compact, subsets of that are homeomorphic also have homeomorphic complements. Thus any wild subspace like the classical construction of Antoine must contain a Cantor set.
Cite
@article{arxiv.2208.11534,
title = {Every countable compact subset of $\mathbb{S}^n$ is tame},
author = {Agelos Georgakopoulos},
journal= {arXiv preprint arXiv:2208.11534},
year = {2022}
}