Theorems · Theorem · functional analysis
tendsto_norm_sub_self_nhdsGE
∀ {E : Type u_4} [inst : SeminormedAddCommGroup E] (x : E),
Filter.Tendsto (fun a => ‖a - x‖) (nhds x) (nhdsWithin 0 (Set.Ici 0))- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 · cited by 3,814
- Filter.Eventuallyproof · cited by 3,134
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- nhdsWithinstatement · cited by 1,912
- Set.Icistatement · cited by 1,070
- norm_nonnegproof · cited by 725
- Set.mem_Iciproof · cited by 37
- tendsto_nhdsWithin_iffproof · cited by 37
- Filter.eventually_trueproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- ContDiffAt.contDiffPointwiseHolderAtproof · cited by 6
- ContDiffPointwiseHolderAt.of_exponent_leproof · cited by 1