Theorems · Theorem · functional analysis
tendsto_norm_inv_mul_self
∀ {E : Type u_4} [inst : SeminormedGroup E] (x : E), Filter.Tendsto (fun a => ‖a⁻¹ * x‖) (nhds x) (nhds 0)- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- nhdsstatement and proof · cited by 5,554
- Norm.normstatement · cited by 5,413
- Filter.Tendstostatement and proof · cited by 3,814
- tendsto_const_nhdsproof · cited by 330
- SeminormedGroupstatement and proof · cited by 250
- Filter.tendsto_idproof · cited by 180
- dist_selfproof · cited by 116
- dist_eq_norm_inv_mulproof · cited by 41
- Filter.Tendsto.distproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- tendsto_norm_inv_mul_self_nhdsNEproof · cited by 1
- tendsto_norm_oneproof · cited by 1
- tendsto_norm_inv_mul_self_nhdsGEproof · cited by 0