Theorems · Theorem · general topology
continuousOn_const
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {s : Set α} {c : β},
ContinuousOn (fun x => c) s- Defined in
- Mathlib.Topology.ContinuousOn
- Cited by
- 96 results in Mathlib
- Foundations
- Depth 71 from the axioms, rests on 813 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 1,411
- Continuous.continuousOnproof · cited by 311
- continuous_constproof · cited by 278
Cited by96
Results whose statement or proof uses this declaration.
- IntervalIntegrable.const_mulproof · cited by 14
- cfc_constproof · cited by 12
- cfcₙ_nonnegproof · cited by 7
- diffContOnCl_constproof · cited by 6
- Orientation.oangle_sign_smul_add_rightproof · cited by 6
- IsPreconnected.intermediate_valueproof · cited by 6
- cfc_const_addproof · cited by 4
- InnerProductSpace.harmonicContOnCl_constproof · cited by 4
- IsPreconnected.prodproof · cited by 3
- exists_ratio_hasDerivAt_eq_ratio_slopeproof · cited by 3
- Complex.continuousOn_one_add_mul_invproof · cited by 3
- IsPreconnected.intermediate_value_Iciproof · cited by 3