Theorems · Theorem · general topology
ContinuousOn.congr
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f g : α → β} {s : Set α},
ContinuousOn f s → Set.EqOn g f s → ContinuousOn g s- Defined in
- Mathlib.Topology.ContinuousOn
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousOnstatement and proof · cited by 1,411
- Set.EqOnstatement and proof · cited by 603
- Set.Subset.reflproof · cited by 66
- ContinuousOn.congr_monoproof · cited by 1
Cited by27
Results whose statement or proof uses this declaration.
- cfcₙ_congrproof · cited by 25
- cfc_congrproof · cited by 20
- ContDiffOn.ftaylorSeriesWithinproof · cited by 11
- ContDiffWithinAt.isSymmSndFDerivWithinAtproof · cited by 6
- continuousOn_congrproof · cited by 5
- EReal.continuous_toENNRealproof · cited by 4
- HasFTaylorSeriesUpToOn.continuousOnproof · cited by 4
- continuousOn_cfc_nnrealproof · cited by 2
- continuousOn_cfcₙ_nnrealproof · cited by 2
- Manifold.IsImmersionAtOfComplement.continuousOnproof · cited by 2
- Real.continuousOn_rpowIntegrand₀₁proof · cited by 2
- Real.continuousOn_rpowIntegrand₀₁_uncurryproof · cited by 2