A strong Kurepa tree
Abstract
We prove that it is consistent that there exists a Kurepa tree $T$ such that ${}^{ω_1}2$ is a continuous image of the topological space $[T]$ consisting of all cofinal branches of $T$ with respect to the cone topologies. This result solves an open problem due to Bergfalk, Chodounský, Guzmán, and Hrušák. We also prove that any Kurepa tree with the above property contains an Aronszajn subtree.
Fields of Study & Subjects
Advanced Topology and Set Theory
Computability
Logic
AI Algorithms
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Publication date
- 3 September 2026
- Language
- EN