Theorems · Theorem · general topology
OpenPartialHomeomorph.injOn
∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
(e : OpenPartialHomeomorph X Y), Set.InjOn (↑e) e.source- Cited by
- 15 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, 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.
- TopologicalSpacestatement and proof · cited by 24,529
- PartialEquiv.sourcestatement · cited by 964
- PartialHomeomorph.toPartialEquivstatement · cited by 917
- OpenPartialHomeomorph.toPartialHomeomorphstatement · cited by 851
- OpenPartialHomeomorph.toFun'statement · cited by 745
- OpenPartialHomeomorphstatement and proof · cited by 664
- Set.InjOnstatement · cited by 543
- Set.LeftInvOn.injOnproof · cited by 15
- OpenPartialHomeomorph.leftInvOnproof · cited by 5
Cited by15
Results whose statement or proof uses this declaration.
- IsLocalHomeomorph.isLocallyInjectiveproof · cited by 6
- IsCoveringMap.isSeparatedMapproof · cited by 4
- IsLocalHomeomorphOn.discreteTopology_of_imageproof · cited by 3
- IsDiscrete.of_openPartialHomeomorphproof · cited by 2
- injOn_pi_polarCoord_symmproof · cited by 2
- IsLocalHomeomorph.exists_lift_nhdsproof · cited by 1
- IsLocalHomeomorph.injOn_localInverseAt_targetproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.injective_expMapproof · cited by 1
- lintegral_comp_polarCoord_symmproof · cited by 1
- ChartedSpace.discreteTopologyproof · cited by 1
- ChartedSpace.t1Spaceproof · cited by 1
- OpenPartialHomeomorph.subtypeRestr_symm_eqOn_of_leproof · cited by 1