Theorems · Theorem · general topology
isLocallyInjective_iff_isOpenMap
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] {f : X → Y},
IsLocallyInjective f ↔ IsOpenMap (toPullbackDiag f)- Defined in
- Mathlib.Topology.SeparatedMap
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
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Cites11
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
- IsOpenMapstatement · cited by 253
- Topology.IsEmbedding.continuousproof · cited by 51
- Topology.IsOpenEmbedding.isOpenMapproof · cited by 50
- Function.Pullbackstatement · cited by 29
- IsLocallyInjectivestatement · cited by 14
- Topology.IsOpenEmbedding.of_continuous_injective_isOpenMapproof · cited by 13
- toPullbackDiagstatement · cited by 9
- Topology.IsEmbedding.toPullbackDiagproof · cited by 4
- injective_toPullbackDiagproof · cited by 3
- IsLocallyInjective_iff_isOpenEmbeddingproof · cited by 1
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