Theorems · Theorem · general topology
Topology.isStrictMap_iff_isEmbedding_kerLift
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Topology.IsStrictMap f ↔ Topology.IsEmbedding (Setoid.kerLift f)A map is a strict map if and only if the canonical injection Quotient (Setoid.ker f) → Y
(Setoid.kerLift f) is an embedding.
- Defined in
- Mathlib.Topology.Maps.Strict.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Topology.IsEmbeddingstatement and proof · cited by 294
- Topology.IsStrictMapstatement · cited by 45
- Setoid.kerstatement · cited by 43
- Topology.IsEmbedding.subtypeValproof · cited by 41
- Topology.IsEmbedding.of_comp_iffproof · cited by 9
- Setoid.kerLiftstatement and proof · cited by 9
- Setoid.quotientKerEquivRangeproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Topology.isEmbedding_iff_isStrictMap_injectiveproof · cited by 1