Toronto space

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In mathematics, in the realm of 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, the upper topology and the lower topology. The only countable Hausdorff topological space is the discrete space.

The Toronto space problem asks for an uncountable Toronto Hausdorff space that is not discrete.