Theorems · Theorem · functional analysis
absorbs_iff_eventually_nhdsNE_zero
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
{s t : Set E}, Absorbs 𝕜 s t ↔ ∀ᶠ (c : 𝕜) in nhdsWithin 0 {0}ᶜ, Set.MapsTo (fun x => c • x) t s- Defined in
- Mathlib.Analysis.LocallyConvex.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Filterproof · cited by 8,121
- Filter.Eventuallystatement and proof · cited by 3,134
- Compl.complstatement and proof · cited by 2,925
- nhdsWithinstatement and proof · cited by 1,912
- Set.MapsTostatement and proof · cited by 732
- NormedDivisionRingstatement and proof · cited by 360
- Bornology.coboundedproof · cited by 162
- Absorbsstatement · cited by 59
- Filter.inv_cobounded₀proof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- absorbs_iff_eventually_nhds_zeroproof · cited by 3
- Absorbs.eventually_nhdsNE_zeroproof · cited by 1