Theorems · Inductive type · general topology
BaireSpace
(X : Type u_1) → [TopologicalSpace X] → Prop
The property BaireSpace α means that the topological space α has the Baire property:
any countable intersection of open dense subsets is dense.
Formulated here when the source space is ℕ.
Use dense_iInter_of_isOpen which works for any countable index type instead.
- Defined in
- Mathlib.Topology.Defs.Basic
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by38
Results whose statement or proof uses this declaration.
- nonempty_interior_of_iUnion_of_closedstatement and proof · cited by 3
- dense_iInter_of_isOpen_natstatement and proof · cited by 3
- dense_of_mem_residualstatement and proof · cited by 3
- dense_sInter_of_isOpenstatement and proof · cited by 3
- mem_residualstatement and proof · cited by 3
- Dense.inter_of_Gδstatement and proof · cited by 2
- BaireSpace.baire_propertystatement and proof · cited by 2
- IsGδ.dense_biUnion_interior_of_closedstatement and proof · cited by 2
- IsGδ.dense_iUnion_interior_of_closedstatement and proof · cited by 2
- dense_iInter_of_Gδstatement and proof · cited by 2
- not_isMeagre_of_isGδ_of_densestatement and proof · cited by 1
- IsOpenQuotientMap.baireSpacestatement and proof · cited by 1