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Toronto space

Type of topological space From Wikipedia, the free encyclopedia

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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]

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