Theorems · Theorem · general topology
Topology.IsEmbedding.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), Topology.IsEmbedding (f i)) → Topology.IsEmbedding (Pi.map f)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 3 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.
Cites7
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.IsEmbeddingstatement and proof · cited by 294
- Topology.IsEmbedding.injectiveproof · cited by 103
- Pi.mapstatement · cited by 60
- Topology.IsEmbedding.toIsInducingproof · cited by 48
- Function.Injective.piMapproof · cited by 5
- Topology.IsInducing.piMapproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Topology.IsEmbedding.matrix_mapproof · cited by 2
- Topology.IsClosedEmbedding.piMapproof · cited by 1
- Topology.IsOpenEmbedding.piMapproof · cited by 1