Theorems · Theorem · general topology
Function.Surjective.isEmbedding_comp
∀ {X : Type u} [inst : TopologicalSpace X] {n : Type u_9} {m : Type u_10} (f : m → n),
Function.Surjective f → Topology.IsEmbedding fun x => x ∘ f- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Filterproof · cited by 8,121
- nhdsproof · cited by 5,554
- iInfproof · cited by 1,690
- Filter.comapproof · cited by 546
- Topology.IsEmbeddingstatement · cited by 294
- InfSetproof · cited by 145
- Function.evalproof · cited by 140
- Filter.comap_comapproof · cited by 69
- nhds_piproof · cited by 29
- Filter.comap_iInfproof · cited by 23
- Topology.isInducing_iff_nhdsproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- CommRingCat.HomTopology.isEmbedding_precomp_of_surjectiveproof · cited by 2