Theorems · Theorem · functional analysis
tendsto_norm_nhdsNE_zero
∀ {E : Type u_4} [inst : NormedAddGroup E], Filter.Tendsto norm (nhdsWithin 0 {0}ᶜ) (nhdsWithin 0 (Set.Ioi 0))See tendsto_norm_zero for a version with full neighborhoods.
- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 157 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.
Cites12
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
- norm_pos_iffproof · cited by 168
- NormedAddGroupstatement and proof · cited by 32
- Filter.Tendsto.infproof · cited by 32
- Filter.tendsto_principal_principalproof · cited by 15
- tendsto_norm_zeroproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Function.Periodic.invQParam_tendstoproof · cited by 3
- Complex.tendsto_norm_tan_of_cos_eq_zeroproof · cited by 3