Add P219 Toronto

properties/P000219.md

@@ -0,0 +1,25 @@
+---
+uid: P000219
+name: Toronto
+refs:
+- mo: 24144
+  name: Is there an uncountable, non-discrete, Hausdorff Toronto space?
+- zb: "0718.54001"
+  name: Open Problems in Topology (van Mill, Reed)
+- zb: "0755.54002"
+  name: Partitioning topological spaces (Weiss)
+- wikipedia: Toronto_space
+  name: Toronto space
+---
+
+Any subspace $Y \subseteq X$ with $|Y|=|X|$ is homeomorphic to $X$.
+
+In {{zb:0755.54002}}, William Weiss notes (as quoted by Andrés E. Caicedo
+in {{mo:24144}}):
+
+> [This] is of course related to the Toronto seminar problem of whether there is
+> an uncountable non-discrete space which is homeomorphic to each of its uncountable subspaces.
+> There are rules for working on this latter problem. The problem can be worked upon only in
+> groups of three or more mathematicians, and it is required that alcohol, preferably beer,
+> be present during this time. Contact anyone in the Toronto Set Theory Seminar for the current
+> status of the problem. It may never be solved."