Theorems · Theorem · general topology
isEmbedding_graph
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Continuous f → Topology.IsEmbedding fun x => (x, f x)- Defined in
- Mathlib.Topology.Constructions.SumProd
- Cited by
- 1 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.
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
- Continuousstatement and proof · cited by 2,592
- Topology.IsEmbeddingstatement · cited by 294
- continuous_idproof · cited by 192
- Continuous.prodMkproof · cited by 127
- continuous_fstproof · cited by 103
- Topology.IsEmbedding.of_compproof · cited by 16
- Topology.IsEmbedding.idproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- CommRingCat.HomTopology.isEmbedding_pushoutproof · cited by 0