Theorems · Theorem · general topology
isLocallyInjective_iff_isOpen_diagonal
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] {f : X → Y},
IsLocallyInjective f ↔ IsOpen (Function.pullbackDiagonal f)- Defined in
- Mathlib.Topology.SeparatedMap
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 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.
Cites17
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
- nhdsproof · cited by 5,554
- Set.preimageproof · cited by 4,946
- IsOpenstatement and proof · cited by 2,400
- SProd.sprodproof · cited by 1,750
- Filter.comapproof · cited by 546
- Set.InjOnproof · cited by 543
- Filter.inter_memproof · cited by 153
- nhds_prod_eqproof · cited by 84
- nhds_inducedproof · cited by 32
- Function.Pullbackstatement and proof · cited by 29
Cited by3
Results whose statement or proof uses this declaration.
- IsLocallyInjective_iff_isOpenEmbeddingproof · cited by 1
- IsLocallyInjective.isOpen_eqLocusproof · cited by 1
- IsLocallyInjective.comp_rightproof · cited by 0