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Polish space (Definition)

A Polish space is a topological space that is homeomorphic to some complete separable metric space.

Equivalently, a topological space is a Polish space if it is separable and completely metrizable.

Examples of Polish spaces are the euclidean space $\mathbb{R}^n$ (with the usual topology), the Cantor space, and the Baire space.




"Polish space" is owned by Koro.
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See Also: topological G-space, Polish group, categories of Polish groups and Polish spaces, spaces homeomorphic to Baire space


Attachments:
Polish spaces up to Borel isomorphism (Theorem) by gel
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Cross-references: Cantor space, usual topology, Euclidean space, completely metrizable, metric space, separable, complete, homeomorphic, topological space
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This is version 2 of Polish space, born on 2005-01-31, modified 2007-11-30.
Object id is 6693, canonical name is PolishSpace.
Accessed 3679 times total.

Classification:
AMS MSC54E50 (General topology :: Spaces with richer structures :: Complete metric spaces)

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