From the authors’ abstract and introduction: “For a space X, let \(X^{0}=X\), let \(X^{\alpha }=\bigcap _{\beta <\alpha }X^{\beta }\). \(X\) is scattered if \(X^{\alpha }=\emptyset \) for some \(\alpha.\) In this case we call the least such \(\alpha \) the Cantor-Bendixson rank of \(X.\) A space \(X\) is called an \( \alpha\)-Toronto space if \(X\) is scattered of Cantor-Bendixson rank \(\alpha \) and is homeomorphic to each of its subspaces of the same rank. We answer a question of Steprans by constructing a countable \(\alpha\)-Toronto space for each \(\alpha \leqq \omega .\) We also construct consistent examples of countable \(\alpha\)-Toronto spaces for each \(\alpha \leqq \omega _{1}\)”.