Theorems · Theorem · functional analysis
tendsto_norm_one
∀ {E : Type u_4} [inst : SeminormedGroup E], Filter.Tendsto (fun a => ‖a‖) (nhds 1) (nhds 0)See tendsto_norm_one for a version with pointed neighborhoods.
- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 156 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.
Cites8
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 and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- Filter.Tendstostatement and proof · cited by 3,814
- SeminormedGroupstatement and proof · cited by 250
- norm_inv'proof · cited by 23
- tendsto_norm_inv_mul_selfproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_norm_nhdsNE_oneproof · cited by 0