Countable Toronto spaces
Volume 163 / 2000
Fundamenta Mathematicae 163 (2000), 143-162 DOI: 10.4064/fm-163-2-143-162
A space X is called an α-Toronto space if X is scattered of Cantor-Bendixson rank α and is homeomorphic to each of its subspaces of the same rank. We answer a question of Steprāns by constructing a countable α-Toronto space for each α ≤ ω. We also construct consistent examples of countable α-Toronto spaces for each $α < ω_1$.