Theorems · Theorem · commutative algebra
tendsto_smoothingFun_of_eq_zero
∀ {R : Type u_1} [inst : CommRing R] (μ : RingSeminorm R) {x : R},
μ x = 0 → Filter.Tendsto (smoothingSeminormSeq μ x) Filter.atTop (nhds (smoothingFun μ x))If μ x = 0, then smoothingFun μ x is the limit of smoothingSeminormSeq μ x.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Realstatement and proof · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- iInfproof · cited by 1,690
- PNatproof · cited by 392
- le_of_eqproof · cited by 366
- zero_powproof · cited by 361
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_smoothingFun_of_map_one_le_oneproof · cited by 7