Theorems · Theorem · complex analysis
FormalMultilinearSeries.ofScalars_eq_zero_of_scalar_zero
∀ {𝕜 : Type u_1} (E : Type u_2) [inst : Field 𝕜] [inst_1 : Ring E] [inst_2 : Algebra 𝕜 E] [inst_3 : TopologicalSpace E]
[inst_4 : IsTopologicalRing E] {c : ℕ → 𝕜} {n : ℕ}, c n = 0 → FormalMultilinearSeries.ofScalars E c n = 0- Defined in
- Mathlib.Analysis.Analytic.OfScalars
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- zero_smulproof · cited by 716
- IsTopologicalRingstatement and proof · cited by 402
- FormalMultilinearSeries.ofScalarsstatement · cited by 68
- ContinuousMultilinearMap.mkPiAlgebraFinproof · cited by 29
Cited by3
Results whose statement or proof uses this declaration.
- Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zeroproof · cited by 1
- FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zeroproof · cited by 0
- FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto_ENNRealproof · cited by 0