Theorems · Theorem · functional analysis
ContinuousLinearMap.differentiable
∀ {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), Differentiable 𝕜 ⇑f- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Linear
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Differentiablestatement · cited by 298
- ContinuousLinearMap.differentiableAtproof · cited by 13
Cited by18
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.hasTemperateGrowthproof · cited by 8
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_ball_re_eqproof · cited by 4
- MDifferentiableWithinAt.clm_postcompproof · cited by 2
- MDifferentiableWithinAt.clm_precompproof · cited by 2
- Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_divproof · cited by 2
- MDifferentiableAt.clm_postcompproof · cited by 2
- MDifferentiableAt.clm_precompproof · cited by 2
- Complex.norm_deriv_le_of_forall_mem_sphere_norm_leproof · cited by 1
- MDifferentiableWithinAt.clm_prodMapproof · cited by 1
- Complex.differentiable_ofRealproof · cited by 1
- Complex.differentiable_reproof · cited by 1
- norm_sub_le_integral_of_norm_deriv_le_of_leproof · cited by 1