Theorems · Theorem · general topology
Continuous.continuousOn
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {s : Set α},
Continuous f → ContinuousOn f s- Defined in
- Mathlib.Topology.ContinuousOn
- Cited by
- 311 results in Mathlib
- Foundations
- Depth 70 from the axioms, rests on 812 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Continuousstatement and proof · cited by 2,592
- ContinuousOnstatement · cited by 1,411
- Set.subset_univproof · cited by 228
- ContinuousOn.monoproof · cited by 156
- continuousOn_univproof · cited by 43
Cited by311
Results whose statement or proof uses this declaration.
- IsCompact.imageproof · cited by 105
- continuousOn_constproof · cited by 96
- Continuous.comp_continuousOnproof · cited by 52
- Continuous.intervalIntegrableproof · cited by 32
- continuousOn_idproof · cited by 30
- Continuous.integrable_of_hasCompactSupportproof · cited by 18
- Differentiable.diffContOnClproof · cited by 15
- NNReal.continuousOn_rpow_constproof · cited by 13
- Topology.IsInducing.isPreconnected_imageproof · cited by 11
- MeromorphicOn.circleIntegrable_log_normproof · cited by 11
- CFC.posPart_sub_negPartproof · cited by 10
- Real.continuousOn_cosproof · cited by 8
Showing the 200 most cited of 311.