Theorems · Definition · functional analysis
Bornology.IsVonNBounded
(𝕜 : Type u_1) → {E : Type u_3} → [SeminormedRing 𝕜] → [SMul 𝕜 E] → [Zero E] → [TopologicalSpace E] → Set E → PropA set s is von Neumann bounded if every neighborhood of 0 absorbs s.
- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 136 results in Mathlib
- Foundations
- Depth 19 from the axioms, rests on 110 definitions · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsproof · cited by 5,554
- SeminormedRingstatement and proof · cited by 446
- Absorbsproof · cited by 59
Cited by166
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.postcompproof · cited by 17
- ContinuousLinearMap.precompproof · cited by 13
- NormedSpace.isVonNBounded_iffstatement and proof · cited by 9
- ContinuousMultilinearMap.toUniformOnFunstatement and proof · cited by 7
- Bornology.IsVonNBounded.imagestatement and proof · cited by 5
- NormedSpace.isVonNBounded_closedBallstatement · cited by 5
- WithSeminorms.isVonNBounded_iff_seminorm_boundedstatement · cited by 4
- TotallyBounded.isVonNBoundedstatement · cited by 4
- NormedSpace.isVonNBounded_ballstatement · cited by 4
- NormedSpace.isVonNBounded_of_isBoundedstatement · cited by 4
- IsCompactOperator.image_subset_compact_of_isVonNBoundedstatement and proof · cited by 4
- gauge_posstatement and proof · cited by 4