Every countable compact subset of \mathbbSⁿ is tame

2022/08/24 by Agelos Georgakopoulos, Georgakopoulos, Agelos
Computer Science · Mathematics · #54C20 #57N35 #57N45 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2208.11534

openalex publication_date 2022/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any two countable, compact, subsets of \mathbbSⁿ, n≥ 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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