Theorems · Theorem · general topology
IsOpen.baireSpace
∀ {X : Type u_1} [inst : TopologicalSpace X] [BaireSpace X] {s : Set X}, IsOpen s → BaireSpace ↑sAn open subset of a Baire space is Baire.
- Defined in
- Mathlib.Topology.Baire.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceBaireSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- IsOpenstatement and proof · cited by 2,400
- BaireSpacestatement and proof · cited by 36
- IsOpen.isOpenEmbedding_subtypeValproof · cited by 32
- Topology.IsOpenEmbedding.baireSpaceproof · cited by 1
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