Theorems · Theorem · general topology
Continuous.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), Continuous (f i)) → Continuous (Pi.map f)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Continuousstatement and proof · cited by 2,592
- Continuous.compproof · cited by 371
- continuous_applyproof · cited by 120
- Pi.mapstatement · cited by 60
- continuous_piproof · cited by 43
Cited by3
Results whose statement or proof uses this declaration.
- IsOpenQuotientMap.piMapproof · cited by 0
- RestrictedProduct.continuous_dom_piproof · cited by 0
- NumberField.InfiniteAdeleRing.denseRange_algebraMapproof · cited by 0