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are nonempty.
* Every open subspace of a Baire space is a Baire space.
* Every dense ''G''_? set in a Baire space is a Baire space. The result need not hold if the G_? set is not dense. See the Examples section.
* Every comeagre set in a Baire space is a Baire space.
* A subset of a Baire space is comeagre if and only if it contains a dense G_? set.
* A closed subspace of a Baire space need not be Baire. See the Examples section.
* If a space contains

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