Theorems · Theorem · complex analysis
FormalMultilinearSeries.partialSum_continuous
∀ {𝕜 : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Semiring 𝕜] [inst_1 : AddCommMonoid E] [inst_2 : AddCommMonoid F]
[inst_3 : Module 𝕜 E] [inst_4 : Module 𝕜 F] [inst_5 : TopologicalSpace E] [inst_6 : TopologicalSpace F]
[inst_7 : ContinuousAdd E] [inst_8 : ContinuousAdd F] [inst_9 : ContinuousConstSMul 𝕜 E]
[inst_10 : ContinuousConstSMul 𝕜 F] (p : FormalMultilinearSeries 𝕜 E F) (n : ℕ), Continuous (p.partialSum n)The partial sums of a formal multilinear series are continuous.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Continuousstatement · cited by 2,592
- Finset.rangeproof · cited by 1,341
- ContinuousConstSMulstatement and proof · cited by 832
- ContinuousAddstatement and proof · cited by 777
- FormalMultilinearSeriesstatement and proof · cited by 615
- continuous_id'proof · cited by 295
- Continuous.comp'proof · cited by 184
- ContinuousMapClass.map_continuousproof · cited by 119
Cited by3
Results whose statement or proof uses this declaration.
- HasFPowerSeriesWithinOnBall.continuousOnproof · cited by 2
- HasFPowerSeriesWithinOnBall.tendsto_partialSum_prodproof · cited by 2
- HasFPowerSeriesAt.eventually_hasSum_of_compproof · cited by 1