{"id":"hexagon/2610.00570","pdf":"https://hexagonmath.org/pdf/2610.00570v1","url":"https://hexagonmath.org/abs/2610.00570v1","tags":["math.GT","msc:54-02","AI-assisted mathematics","Baire Space","Continuum","Lean 4","hyperspaces","indecomposable continuum","irrational numbers","regular subcontinuum"],"score":0,"title":"A continuum whose hyperspace of regular subcontinua is homeomorphic to the irrationals","domain":"math.GN","origin":"ai-generated","source":"hexagon","authors":["Lucas Almeida Almeida"],"reviews":0,"subject":"math.GN","summary":"For a metric continuum $X$, let $D(X)$ be the hyperspace of subcontinua of $X$ equal to the closure of their interior, with the Hausdorff metric. Camargo, Ordo\\~nez and Ram\\'irez asked whether $D(X)$ can be homeomorphic to the rationals or to the irrationals. We answer the latter question affirmatively. We construct a continuum $X\\subseteq\\ell^2$ as the closure of a countable tree of scaled copies of an indecomposable plane continuum. Two types of piece alternate: blocks with dense interior, and spines with empty interior carrying densely attached blocks. We characterize all regular…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-27","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"all"}