Theorems · Theorem · commutative algebra
PowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_isNilpotent
∀ {R : Type u_1} [inst : TopologicalSpace R] [inst_1 : CommSemiring R] {f : PowerSeries R},
IsNilpotent (PowerSeries.constantCoeff f) → Filter.Tendsto (fun n => f ^ n) Filter.atTop (nhds 0)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCommSemiring
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Cites11
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
- PowerSeriesstatement and proof · cited by 797
- IsNilpotentstatement and proof · cited by 248
- PowerSeries.constantCoeffstatement and proof · cited by 126
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