Theorems · Definition · commutative algebra
IsTopologicallyNilpotent
{R : Type u_1} → [MonoidWithZero R] → [TopologicalSpace R] → R → PropAn element is topologically nilpotent if its powers converge to 0.
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- MonoidWithZerostatement and proof · cited by 456
Cited by26
Results whose statement or proof uses this declaration.
- PowerSeries.HasEvalproof · cited by 28
- MvPowerSeries.HasEval.hpowstatement · cited by 6
- MvPowerSeries.hasSubst_iff_hasEval_of_discreteTopologyproof · cited by 5
- MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_isNilpotentstatement · cited by 4
- IsTopologicallyNilpotent.mul_leftstatement and proof · cited by 2
- topologicalNilradicalproof · cited by 2
- IsTopologicallyNilpotent.addstatement and proof · cited by 2
- IsTopologicallyNilpotent.mapstatement and proof · cited by 2
- IsTopologicallyNilpotent.mul_left_of_commutestatement and proof · cited by 1
- IsTopologicallyNilpotent.mul_right_of_commutestatement and proof · cited by 1
- IsTopologicallyNilpotent.zerostatement · cited by 1
- MvPowerSeries.LinearTopology.isTopologicallyNilpotent_of_constantCoeffstatement and proof · cited by 1