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},
Set.EqOn g f s → (ContinuousOn g s ↔ ContinuousOn f s)- Defined in
- Mathlib.Topology.ContinuousOn
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 67 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.EqOn.symmproof · cited by 41
- ContinuousOn.congrproof · cited by 27
Cited by5
Results whose statement or proof uses this declaration.
- IsLocalHomeomorphOn.mkproof · cited by 5
- hasFTaylorSeriesUpToOn_zero_iffproof · cited by 1
- continuousOn_floorproof · cited by 1
- intervalIntegral.continuousOn_primitiveproof · cited by 1
- continuousOn_ceilproof · cited by 0