Theorems · Theorem · functional analysis
tendsto_norm_neg_add_self_nhdsNE
∀ {E : Type u_4} [inst : NormedAddGroup 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 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Norm.normstatement · cited by 5,413
- Filter.Tendstostatement · cited by 3,814
- Compl.complstatement and proof · cited by 2,925
- nhdsWithinstatement · cited by 1,912
- Set.Ioistatement · cited by 1,463
- Set.mem_singleton_iffproof · cited by 172
- norm_pos_iffproof · cited by 168
- Set.mem_compl_iffproof · cited by 53
- NormedAddGroupstatement and proof · cited by 32
- Filter.Tendsto.infproof · cited by 32
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_norm_sub_self_nhdsNEproof · cited by 1