Theorems · Theorem · general topology
Topology.IsQuotientMap.of_comp_iff
∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} {f : X → Y} {g : Y → Z} [inst : TopologicalSpace X]
[inst_1 : TopologicalSpace Y] [inst_2 : TopologicalSpace Z],
Topology.IsQuotientMap f → (Topology.IsQuotientMap (g ∘ f) ↔ Topology.IsQuotientMap g)- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 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
- Topology.IsQuotientMapstatement and proof · cited by 124
- Topology.IsQuotientMap.isCoinducingproof · cited by 35
- Topology.IsCoinducingproof · cited by 31
- Topology.IsQuotientMap.surjectiveproof · cited by 24
- Function.Surjective.of_comp_iffproof · cited by 7
- Topology.isQuotientMap_iffproof · cited by 5
- Topology.IsCoinducing.of_comp_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsQuotientMap.isStrictMap_iffproof · cited by 8