Theorems · Theorem · functional analysis
tendsto_norm_sub_self_nhdsNE
∀ {E : Type u_7} [inst : NormedAddCommGroup E] (a : E),
Filter.Tendsto (fun x => ‖x - a‖) (nhdsWithin a {a}ᶜ) (nhdsWithin 0 (Set.Ioi 0))- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
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.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Norm.normstatement · cited by 5,413
- Filter.Tendstostatement and proof · cited by 3,814
- Compl.complstatement and proof · cited by 2,925
- nhdsWithinstatement and proof · cited by 1,912
- Set.Ioistatement and proof · cited by 1,463
- norm_neg_addproof · cited by 12
- tendsto_norm_neg_add_self_nhdsNEproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Filter.IsBoundedUnder.isLittleO_sub_self_invproof · cited by 2