Theorems · Theorem · functional analysis
ContinuousLinearMap.differentiableWithinAt
∀ {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} {s : Set E}, DifferentiableWithinAt 𝕜 (⇑f) s x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Linear
- Cited by
- 1 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- 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
- DifferentiableWithinAtstatement · cited by 453
- DifferentiableAt.differentiableWithinAtproof · cited by 96
- ContinuousLinearMap.differentiableAtproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.mdifferentiableWithinAtproof · cited by 0