Theorems · Theorem · general topology
Topology.isEmbedding_iff_isStrictMap_injective
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Topology.IsEmbedding f ↔ Topology.IsStrictMap f ∧ Function.Injective fEmbeddings are precisely injective strict maps.
- Defined in
- Mathlib.Topology.Maps.Strict.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Homeomorphproof · cited by 725
- Homeomorph.symmproof · cited by 365
- Topology.IsEmbeddingstatement and proof · cited by 294
- Topology.IsEmbedding.injectiveproof · cited by 103
- Homeomorph.isEmbeddingproof · cited by 73
- Homeomorph.transproof · cited by 49
- Topology.IsStrictMapstatement and proof · cited by 45
- Setoid.kerproof · cited by 43
- Topology.IsEmbedding.compproof · cited by 29
- Homeomorph.Quotient.congrRightproof · cited by 2
- Topology.IsEmbedding.isStrictMapproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddMonoidHom.isStrictMap_iff_isEmbedding_kerLiftproof · cited by 1