Theorems · Theorem · global analysis
ContinuousMultilinearMap.hasStrictFDerivAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {ι : Type u_2} {E : ι → Type u_3} [inst_3 : (i : ι) → NormedAddCommGroup (E i)]
[inst_4 : (i : ι) → NormedSpace 𝕜 (E i)] [inst_5 : Fintype ι] (f : ContinuousMultilinearMap 𝕜 E F) (x : (i : ι) → E i)
[inst_6 : DecidableEq ι], HasStrictFDerivAt (⇑f) (f.linearDeriv x) x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- RingHom.idproof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- AddCommGroupproof · cited by 12,871
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Fintypestatement and proof · cited by 7,736
- ContinuousLinearMapproof · cited by 5,352
- zero_addproof · cited by 2,366
- ContinuousMultilinearMapstatement and proof · cited by 1,016
Cited by4
Results whose statement or proof uses this declaration.
- ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMapproof · cited by 4
- ContinuousMultilinearMap.hasStrictFDerivAt_uncurryproof · cited by 2
- ContinuousMultilinearMap.hasFDerivAtproof · cited by 2
- ContinuousAlternatingMap.hasStrictFDerivAtproof · cited by 0