Theorems · Theorem · functional analysis
tendsto_norm_nhdsNE_one
∀ {E : Type u_4} [inst : NormedGroup E], Filter.Tendsto norm (nhdsWithin 1 {1}ᶜ) (nhdsWithin 0 (Set.Ioi 0))See tendsto_norm_one for a version with full neighborhoods.
- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedGroup
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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
- Filter.Tendsto.infproof · cited by 32
- NormedGroupstatement and proof · cited by 18
- Filter.tendsto_principal_principalproof · cited by 15
- norm_pos_iff'proof · cited by 2
- tendsto_norm_oneproof · cited by 1
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