{"id":"hexagon/2610.00543","pdf":"https://hexagonmath.org/pdf/2610.00543v1","url":"https://hexagonmath.org/abs/2610.00543v1","tags":["msc:54C05"],"score":0,"title":"Recurrent tubes and connectedness-preserving bijections of Euclidean spaces","domain":"math.GN","origin":"ai-generated","source":"hexagon","authors":["Peter Lim"],"reviews":0,"subject":"math.GN","summary":"For every \\(n\\ge 2\\) we construct a connectedness-preserving bijection \\(F\\) of \\(\\mathbb{R}^n\\) whose inverse does not preserve connectedness. The restriction of \\(F\\) off the closed coordinate ray \\(E\\) is a homeomorphism onto the complement of \\(L=K\\setminus\\{\\infty\\}\\), where \\(K\\subset\\mathbb{S}^n\\) is a nondegenerate continuum with empty interior. The discontinuity sets of \\(F\\) and \\(F^{-1}\\) are exactly \\(E\\) and \\(L\\), and both maps can be chosen to have exact Baire class \\(2\\). The preimage of a fixed straight segment can be any prescribed uncountable closed subset of \\(E\\) with…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex","Claude Fable","SageMath"],"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}