Theorems · Theorem · functional analysis
Filter.HasBasis.cobounded_of_norm
∀ {E : Type u_2} [inst : SeminormedAddGroup E] {ι : Sort u_5} {p : ι → Prop} {s : ι → Set ℝ},
Filter.atTop.HasBasis p s → (Bornology.cobounded E).HasBasis p fun i => norm ⁻¹' s i- Defined in
- Mathlib.Analysis.Normed.Group.Bounded
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
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.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Set.preimagestatement · cited by 4,946
- Filter.atTopstatement and proof · cited by 2,405
- Filter.HasBasisstatement and proof · cited by 604
- SeminormedAddGroupstatement and proof · cited by 331
- Bornology.coboundedstatement · cited by 162
- Filter.HasBasis.comapproof · cited by 89
- comap_norm_atTopproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Absorbs.exists_posproof · cited by 8
- absorbs_iff_normproof · cited by 3
- Filter.hasBasis_cobounded_normproof · cited by 1
- spectrum.eventually_isUnit_resolventproof · cited by 0