Theorems · Theorem · functional analysis
NormedAddCommGroup.uniformity_basis_dist
∀ {E : Type u_5} [inst : SeminormedAddCommGroup E],
(uniformity E).HasBasis (fun ε => 0 < ε) fun ε => {p | ‖p.1 - p.2‖ < ε}- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 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.
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
- Norm.normstatement · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- uniformitystatement and proof · cited by 765
- Filter.HasBasisstatement and proof · cited by 604
- norm_neg_addproof · cited by 12
- NormedAddGroup.uniformity_basis_distproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- lp.tendsto_lp_of_tendsto_piproof · cited by 0