Theorems · Theorem · general topology
IsOpenQuotientMap.iff_isOpenMap_isQuotientMap
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
IsOpenQuotientMap f ↔ IsOpenMap f ∧ Topology.IsQuotientMap f- Defined in
- Mathlib.Topology.Maps.OpenQuotient
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- IsOpenMapstatement and proof · cited by 253
- Topology.IsQuotientMapstatement and proof · cited by 124
- IsOpenQuotientMapstatement and proof · cited by 65
- Topology.IsQuotientMap.surjectiveproof · cited by 24
- IsOpenQuotientMap.isOpenMapproof · cited by 16
- Topology.IsQuotientMap.continuousproof · cited by 14
- IsOpenQuotientMap.isQuotientMapproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- IsOpenQuotientMap.of_isOpenMap_isQuotientMapproof · cited by 0