Countable Toronto spaces

Tom 163 / 2000

Gary Gruenhage, J. Tach Moore 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 $α < ω_1$.


  • Gary Gruenhage
  • J. Tach Moore

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