Theorems · Theorem · general topology
IsOpenMap.isQuotientMap
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
IsOpenMap f → Continuous f → Function.Surjective f → Topology.IsQuotientMap fA continuous surjective open map is a quotient map.
- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Continuousstatement and proof · cited by 2,592
- IsOpenproof · cited by 2,400
- IsOpenMapstatement and proof · cited by 253
- IsOpen.preimageproof · cited by 147
- Topology.IsQuotientMapstatement · cited by 124
- Function.Surjective.image_preimageproof · cited by 16
- Topology.IsCoinducing.of_isOpen_preimage_iff_isOpenproof · cited by 6
- Topology.isQuotientMap_iffproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- IsOpenQuotientMap.isQuotientMapproof · cited by 12
- IsOpenMap.isStrictMapproof · cited by 2
- IsHomeomorphicTrivialFiberBundle.isQuotientMap_projproof · cited by 2
- IsCoveringMap.isQuotientMapproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.isConnected_preimageproof · cited by 1
- Complex.isAddQuotientCoveringMap_expproof · cited by 1
- Pi.locallyConnectedSpace_iffproof · cited by 0
- Pi.locallyPathConnectedSpace_iffproof · cited by 0
- ContinuousLinearMap.isQuotientMapproof · cited by 0
- FiberBundle.isQuotientMap_projproof · cited by 0