Theorems · Theorem · functional analysis
NormedCommGroup.nhds_basis_norm_lt
∀ {E : Type u_5} [inst : SeminormedCommGroup E] (x : E), (nhds x).HasBasis (fun ε => 0 < ε) fun ε => {y | ‖y / x‖ < ε}- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Set.ofPredstatement and proof · cited by 6,101
- nhdsstatement and proof · cited by 5,554
- Norm.normstatement · cited by 5,413
- Filter.HasBasisstatement and proof · cited by 604
- SeminormedCommGroupstatement and proof · cited by 191
- norm_inv_mulproof · cited by 5
- NormedGroup.nhds_basis_norm_ltproof · cited by 3
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