Theorems · Theorem · functional analysis
ContinuousLinearMap.differentiableAt
∀ {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 →L[𝕜] F) {x : E}, DifferentiableAt 𝕜 (⇑f) x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Linear
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 167 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.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement and proof · cited by 5,352
- DifferentiableAtstatement · cited by 617
- HasFDerivAt.differentiableAtproof · cited by 83
- ContinuousLinearMap.hasFDerivAtproof · cited by 38
Cited by13
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.differentiableproof · cited by 18
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_ball_re_eqproof · cited by 4
- mdifferentiableAt_localFrameCoeffproof · cited by 4
- HarmonicAt.differentiableAt_complex_partialproof · cited by 3
- not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filterproof · cited by 2
- DifferentiableAt.mem_interior_convex_of_surjective_fderivproof · cited by 2
- ContinuousLinearMap.fderivWithinproof · cited by 1
- ContinuousLinearMap.differentiableWithinAtproof · cited by 1
- HasCompactSupport.enorm_le_lintegral_Ici_derivproof · cited by 1
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_univ_re_eqproof · cited by 1
- fderivWithin_restrictScalars_compproof · cited by 1
- ContDiffPointwiseHolderAt.continuousLinearMap_compproof · cited by 1