Theorems · Theorem · commutative algebra
MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_zero
∀ {σ : Type u_1} {R : Type u_2} [inst : TopologicalSpace R] [inst_1 : CommSemiring R] {f : MvPowerSeries σ R},
MvPowerSeries.constantCoeff f = 0 → Filter.Tendsto (fun n => f ^ n) Filter.atTop (nhds 0)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- TopologicalSpacestatement and proof · cited by 24,529
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- MvPowerSeriesstatement and proof · cited by 659
- IsNilpotentproof · cited by 248
- MvPowerSeries.constantCoeffstatement and proof · cited by 98
- IsNilpotent.zeroproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- MvPowerSeries.HasEval.Xproof · cited by 4