Theorems · Theorem · general topology
Topology.IsEmbedding.prodMap
∀ {X : Type u} {Y : Type v} {W : Type u_1} {Z : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
[inst_2 : TopologicalSpace Z] [inst_3 : TopologicalSpace W] {f : X → Y} {g : Z → W},
Topology.IsEmbedding f → Topology.IsEmbedding g → Topology.IsEmbedding (Prod.map f g)- Defined in
- Mathlib.Topology.Constructions.SumProd
- Cited by
- 6 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.IsInducingproof · cited by 266
- Topology.IsEmbedding.injectiveproof · cited by 103
- Topology.IsEmbedding.isInducingproof · cited by 47
- Function.Injective.prodMapproof · cited by 9
- Topology.IsInducing.prodMapproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- Topology.IsOpenEmbedding.prodMapproof · cited by 3
- Topology.IsClosedEmbedding.prodMapproof · cited by 1
- Topology.IsEmbedding.units_mapproof · cited by 1
- CommRingCat.HomTopology.isEmbedding_pushoutproof · cited by 0
- Manifold.IsSmoothEmbedding.prodMapproof · cited by 0
- Topology.IsEmbedding.addUnits_mapproof · cited by 0