Theorems · Theorem · general topology
IsOpenQuotientMap.piMap
∀ {ι : Type u_5} {A : ι → Type u_6} {B : ι → Type u_7} [T : (i : ι) → TopologicalSpace (A i)]
[inst : (i : ι) → TopologicalSpace (B i)] {f : (i : ι) → A i → B i},
(∀ (i : ι), IsOpenQuotientMap (f i)) → IsOpenQuotientMap (Pi.map f)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Filter.Eventually.of_forallproof · cited by 526
- IsOpenQuotientMapstatement and proof · cited by 65
- Pi.mapstatement · cited by 60
- IsOpenQuotientMap.isOpenMapproof · cited by 16
- IsOpenQuotientMap.surjectiveproof · cited by 16
- IsOpenQuotientMap.continuousproof · cited by 15
- Function.Surjective.piMapproof · cited by 6
- Continuous.piMapproof · cited by 3
- IsOpenMap.piMapproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.