Theorems · Theorem · general topology
PartialHomeomorph.continuousOn_invFun
∀ {X : Type u_7} {Y : Type u_8} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
(self : PartialHomeomorph X Y), ContinuousOn self.invFun self.target- Defined in
- Mathlib.Topology.PartialHomeomorph.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- ContinuousOnstatement · cited by 1,411
- PartialHomeomorph.toPartialEquivstatement · cited by 917
- PartialEquiv.targetstatement · cited by 650
- PartialHomeomorphstatement and proof · cited by 73
- PartialEquiv.invFunstatement · cited by 43
Cited by10
Results whose statement or proof uses this declaration.
- PartialHomeomorph.symmproof · cited by 38
- OpenPartialHomeomorph.continuousOn_symmproof · cited by 8
- OpenPartialHomeomorph.isOpen_image_of_subset_sourceproof · cited by 6
- IsLocalHomeomorphOn.mkproof · cited by 5
- IsCoveringMap.exists_path_liftsproof · cited by 4
- OpenPartialHomeomorph.contDiffAt_symmproof · cited by 3
- IsEvenlyCovered.of_trivializationproof · cited by 2
- IsLocalHomeomorph.exists_lift_nhdsproof · cited by 1
- IsLocalHomeomorph.isTopologicalBasisproof · cited by 0
- PartialHomeomorph.continuousOn_symmproof · cited by 0