Open retractions of indecomposable continua, II
Volume 180 / 2026
Colloquium Mathematicum 180 (2026), 13-19
MSC: Primary 54F15; Secondary 54C10
DOI: 10.4064/cm9677-10-2025
Published online: 11 December 2025
Abstract
This paper is a sequel to [Colloq. Math. 148 (2017), 191–194]. Given an arbitrary continuum $Z$, we consider the class of all indecomposable continua that contain $Z$ as an open retract with Cantor set fibers and are closures of countable unions of topological copies of $Z$. We prove that this class admits no common model. Furthermore, when $Z$ is tree-like, we show that there exists a subclass of such continua that admits no common model and whose members are all tree-like.
