Theorems · Theorem · global analysis
Differentiable.continuous
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
[inst_6 : TopologicalSpace F] {f : E → F} [ContinuousAdd E] [ContinuousSMul 𝕜 E] [ContinuousAdd F]
[ContinuousSMul 𝕜 F], Differentiable 𝕜 f → Continuous f- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Basic
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Continuousstatement · cited by 2,592
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- Differentiablestatement and proof · cited by 298
- continuous_iff_continuousAtproof · cited by 139
- DifferentiableAt.continuousAtproof · cited by 28
Cited by28
Results whose statement or proof uses this declaration.
- continuous_circleMapproof · cited by 17
- Differentiable.diffContOnClproof · cited by 15
- continuous_sigmoidproof · cited by 2
- WeakFEPair.Λ_residue_zeroproof · cited by 2
- Complex.norm_le_of_forall_mem_frontier_norm_leproof · cited by 2
- riemannZeta₁_ne_zero_of_near_oneproof · cited by 2
- HurwitzZeta.hurwitzZetaEven_residue_oneproof · cited by 2
- DirichletCharacter.LFunction_changeLevelproof · cited by 1
- HurwitzZeta.hurwitzZeta_residue_oneproof · cited by 1
- monotone_of_deriv_nonnegproof · cited by 1
- Differentiable.isExactOn_univproof · cited by 1