Theorems · Theorem · general topology
IsOpenQuotientMap.baireSpace
∀ {X : Type u_1} [inst : TopologicalSpace X] [BaireSpace X] {Y : Type u_4} [inst_2 : TopologicalSpace Y] {f : X → Y},
IsOpenQuotientMap f → BaireSpace YIf f is an open quotient map and X is Baire, then Y is Baire.
- Defined in
- Mathlib.Topology.Baire.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.preimageproof · cited by 4,946
- IsOpenproof · cited by 2,400
- Set.iInterproof · cited by 1,084
- Denseproof · cited by 359
- IsOpenQuotientMapstatement and proof · cited by 65
- Continuous.isOpen_preimageproof · cited by 51
- BaireSpacestatement and proof · cited by 36
- IsOpenQuotientMap.continuousproof · cited by 15
- dense_iInter_of_isOpen_natproof · cited by 3
- IsOpenQuotientMap.dense_preimage_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Homeomorph.baireSpaceproof · cited by 1