Theorems · Definition · general topology
Absorbs
(M : Type u_1) → {α : Type u_2} → [Bornology M] → [SMul M α] → Set α → Set α → PropA set s absorbs another set t if t is contained in all scalings of s
by all but a bounded set of elements.
- Defined in
- Mathlib.Topology.Bornology.Absorbs
- Cited by
- 59 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Filter.Eventuallyproof · cited by 3,134
- Bornologystatement and proof · cited by 188
- Bornology.coboundedproof · cited by 162
Cited by62
Results whose statement or proof uses this declaration.
- Bornology.IsVonNBoundedproof · cited by 136
- Absorbentproof · cited by 60
- Absorbs.exists_posstatement and proof · cited by 8
- Absorbs.mono_rightstatement and proof · cited by 6
- Absorbs.mono_leftstatement and proof · cited by 5
- NormedSpace.isVonNBounded_of_isBoundedproof · cited by 4
- Filter.absorbingproof · cited by 3
- Absorbent.absorbsstatement · cited by 3
- absorbs_iff_eventually_nhds_zerostatement and proof · cited by 3
- absorbs_iff_normstatement · cited by 3
- Absorbs.addstatement and proof · cited by 3
- Set.Finite.absorbs_biUnionstatement · cited by 3