Theorems · Theorem · general topology
IsLocallyInjective_iff_isOpenEmbedding
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] {f : X → Y},
IsLocallyInjective f ↔ Topology.IsOpenEmbedding (toPullbackDiag f)- Defined in
- Mathlib.Topology.SeparatedMap
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.rangeproof · cited by 4,705
- IsOpenproof · cited by 2,400
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- Topology.IsOpenEmbedding.isOpen_rangeproof · cited by 33
- Function.Pullbackstatement and proof · cited by 29
- IsLocallyInjectivestatement · cited by 14
- toPullbackDiagstatement and proof · cited by 9
- Topology.IsEmbedding.toPullbackDiagproof · cited by 4
- isLocallyInjective_iff_isOpen_diagonalproof · cited by 3
- range_toPullbackDiagproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- isLocallyInjective_iff_isOpenMapproof · cited by 0