Theorems · Theorem · several complex variables
ContinuousMultilinearMap.cpolynomialAt
∀ {𝕜 : Type u_1} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {ι : Type u_5} {Em : ι → Type u_6} [inst_3 : (i : ι) → NormedAddCommGroup (Em i)]
[inst_4 : (i : ι) → NormedSpace 𝕜 (Em i)] [inst_5 : Fintype ι] (f : ContinuousMultilinearMap 𝕜 Em F)
{x : (i : ι) → Em i}, CPolynomialAt 𝕜 (⇑f) x- Defined in
- Mathlib.Analysis.Analytic.CPolynomial
- Cited by
- 3 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.
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Fintypestatement and proof · cited by 7,736
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- CPolynomialAtstatement · cited by 28
- Metric.eball_topproof · cited by 7
- HasFiniteFPowerSeriesOnBall.cpolynomialAt_of_memproof · cited by 5
- ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBallproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- ContinuousMultilinearMap.contDiffAtproof · cited by 1
- ContinuousMultilinearMap.analyticAtproof · cited by 1
- ContinuousMultilinearMap.cpolynomialOnproof · cited by 1