Timeline for Is there an uncountable, non-discrete, Hausdorff Toronto space?
Current License: CC BY-SA 2.5
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| Feb 4, 2011 at 19:56 | comment | added | Apollo | From the 7th status report: in G. Gruenhage, J.T. Moore, Countable Toronto spaces, Fund. Math. 163 (2) (2000) 143–162, they show that there is an $\omega$-Toronto space, where an $\alpha$-Toronto space is a scattered space of Cantor-Bendixson rank $\alpha$ which is homeomorphic to each of its subspaces of rank $\alpha$. They constructed countable $\alpha$-Toronto spaces for each $\alpha\lt\omega$. Gruenhage also constructed consistent examples of countable $\alpha$-Toronto spaces for each $\alpha<\omega_1$. | |
| Feb 2, 2011 at 22:03 | history | answered | Apollo | CC BY-SA 2.5 |