Theorems · Theorem · functional analysis
SeminormedGroup.disjoint_nhds
∀ {E : Type u_5} [inst : SeminormedGroup E] (x : E) (f : Filter E),
Disjoint (nhds x) f ↔ ∃ δ > 0, ∀ᶠ (y : E) in f, δ ≤ ‖y⁻¹ * x‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Filterstatement and proof · cited by 8,121
- Set.ofPredproof · cited by 6,101
- nhdsstatement · cited by 5,554
- Norm.normstatement and proof · cited by 5,413
- Filter.Eventuallystatement · cited by 3,134
- Disjointstatement · cited by 2,201
- SeminormedGroupstatement and proof · cited by 250
- Filter.HasBasis.disjoint_iff_leftproof · cited by 11
- NormedGroup.nhds_basis_norm_ltproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- SeminormedGroup.disjoint_nhds_oneproof · cited by 0