Theorems · Theorem · general topology
PartialHomeomorph.continuousOn_toFun
∀ {X : Type u_7} {Y : Type u_8} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
(self : PartialHomeomorph X Y), ContinuousOn (↑self.toPartialEquiv) self.source- Defined in
- Mathlib.Topology.PartialHomeomorph.Defs
- Cited by
- 10 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
- PartialEquiv.sourcestatement · cited by 964
- PartialHomeomorph.toPartialEquivstatement · cited by 917
- PartialEquiv.toFunstatement · cited by 821
- PartialHomeomorphstatement and proof · cited by 73
Cited by11
Results whose statement or proof uses this declaration.
- PartialHomeomorph.symmproof · cited by 38
- OpenPartialHomeomorph.continuousOnproof · cited by 10
- IsLocalHomeomorphOn.mkproof · cited by 5
- IsCoveringMap.isSeparatedMapproof · cited by 4
- IsLocalHomeomorphOn.discreteTopology_of_imageproof · cited by 3
- StructureGroupoid.compatible_of_mem_maximalAtlasproof · cited by 2
- IsEvenlyCovered.of_trivializationproof · cited by 2
- mdifferentiableOn_iff_targetproof · cited by 1
- contMDiffOn_iff_targetproof · cited by 1
- Bundle.Trivialization.continuousOnproof · cited by 1
- PartialHomeomorph.continuousOnproof · cited by 0