On the structure of countable hyperspaces of regular subcontinua
Main result. If X is a metric continuum whose hyperspace D(X) of regular subcontinua is countable, then D(X) is a Gδ subset of C(X), hence completely metrizable and scattered, with dense isolated points. In particular D(X) is never homeomorphic to the rationals. This answers the rational case of a question of Ramírez Angarita (2023, Pregunta 3.2.14) and of Camargo, Ordoñez and Ramírez (Appl. Gen. Topol. 25 (2024), Question 3.26); the irrational case was answered in the companion repository. Every theorem of the paper is formalized in Lean 4 with Mathlib
Authors
- Lucas Alves de Almeida Lucas Alves de Almeida (ORCID: https://orcid.org/0009-0009-5606-7291)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-11-11
- DOI
- https://doi.org/10.5281/zenodo.24144776
- Primary Topic
- Advanced Topology and Set Theory
- Type
- preprint