Toronto space
Type of topological space / From Wikipedia, the free encyclopedia
In mathematics, in the realm of point-set topology, a Toronto space is a topological space that is homeomorphic to every proper subspace of the same cardinality.
There are five homeomorphism classes of countable Toronto spaces, namely: the discrete topology, the indiscrete topology, the cofinite topology and the upper and lower topologies on the natural numbers. The only countable Hausdorff Toronto space is the discrete space.[1]
The Toronto space problem asks for an uncountable Toronto Hausdorff space that is not discrete.[2]