Properties
- (Alexandrov's theorem) If X is Polish then so is any Gδ subset of X.
- (Cantor–Bendixson theorem) If X is Polish then any closed subset of X can be written as the disjoint union of a perfect subset and a countable subset.
The converse of Alexandrov's theorem is true as well: if a subspace S of a Polish space X is Polish, then it is a Gδ subset of X.
Read more about this topic: Polish Space
Famous quotes containing the word properties:
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—John Locke (1632–1704)
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