Bosserhoff, Volker; Hertling, Peter Effective subsets under homeomorphisms of \(\mathbb{R}^n\). (English) Zbl 1337.03066 Inf. Comput. 245, 197-212 (2015). This paper studies the (non-)preservation of computability of a compact subset of \(\mathbb{R}^n\) under arbitrary (i.e. not necessarily computable) homeomorphisms.Strengthening the result that any non-empty computable compact subset of \(\mathbb{R}^n\) is homeomorphic to a non-computable compact subset of \(\mathbb{R}^n\), the paper proves a conjecture of Braverman. Namely, there is a computably (co-)enumerable compact subset K of \([0,1]^n\) such that under no homeomorphism \(f\) on \(\mathbb{R}^n\) do we have that \(f(K)\) is computable. Reviewer: Danko Ilik (Paris) MSC: 03D78 Computation over the reals, computable analysis 03F60 Constructive and recursive analysis Keywords:computability; real numbers; computable analysis; Euclidean space; compact subset; computable subset; computably enumerable subset; computably coenumerable subset; homeomorphism; arithmetical hierarchy PDF BibTeX XML Cite \textit{V. Bosserhoff} and \textit{P. Hertling}, Inf. Comput. 245, 197--212 (2015; Zbl 1337.03066) Full Text: DOI References: [1] Brattka, V., Plottable real number functions and the computable graph theorem, SIAM J. Comput., 38, 1, 303-328, (2008) · Zbl 1165.03052 [2] Rogers, H., Theory of recursive functions and effective computability, (1987), MIT Press Cambridge · Zbl 0183.01401 [3] Weihrauch, K., Computable analysis: an introduction, (2000), Springer Berlin · Zbl 0956.68056 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.