Theorems · Theorem · global analysis
DifferentiableOn.continuousOn
∀ {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} {s : Set E} [ContinuousAdd E] [ContinuousSMul 𝕜 E] [ContinuousAdd F]
[ContinuousSMul 𝕜 F], DifferentiableOn 𝕜 f s → ContinuousOn f s- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Basic
- Cited by
- 32 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.
- Setstatement and proof · cited by 53,352
- 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
- ContinuousOnstatement · cited by 1,411
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- DifferentiableOnstatement and proof · cited by 419
- DifferentiableWithinAt.continuousWithinAtproof · cited by 9
Cited by32
Results whose statement or proof uses this declaration.
- DifferentiableOn.diffContOnClproof · cited by 8
- Complex.differentiableOn_update_limUnder_of_isLittleOproof · cited by 4
- Complex.norm_eqOn_of_isPreconnected_of_isMaxOnproof · cited by 3
- MeasureTheory.measurableEmbedding_of_fderivWithinproof · cited by 3
- MeasureTheory.measurable_image_of_fderivWithinproof · cited by 3
- IsOpen.exists_is_const_of_fderiv_eq_zeroproof · cited by 3
- MeasureTheory.restrict_map_withDensity_abs_det_fderiv_eq_addHaarproof · cited by 3
- Complex.dist_le_div_mul_dist_of_mapsTo_ballproof · cited by 3
- not_differentiableWithinAt_of_deriv_tendsto_atTop_Ioiproof · cited by 2
- convexOn_of_deriv2_nonnegproof · cited by 2
- concaveOn_of_deriv2_nonposproof · cited by 2
- Complex.integral_boundary_rect_eq_zero_of_differentiableOnproof · cited by 2