Theorems · Theorem · functional analysis
NormedSpace.isVonNBounded_closedBall
∀ (𝕜 : Type u_1) (E : Type u_3) [inst : NormedField 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] (r : ℝ), Bornology.IsVonNBounded 𝕜 (Metric.closedBall 0 r)
- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- NormedSpacestatement and proof · cited by 12,499
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NormedFieldstatement and proof · cited by 1,084
- Metric.closedBallstatement · cited by 704
- Bornology.IsVonNBoundedstatement · cited by 136
- Metric.isBounded_closedBallproof · cited by 19
- NormedSpace.isVonNBounded_of_isBoundedproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- IsCompactOperator.image_closedBall_subset_compactproof · cited by 3
- isClosed_setOfPred_isCompactOperatorproof · cited by 3
- IsCompactOperator.isCompact_closure_image_closedBallproof · cited by 2
- NormedSpace.isBounded_iff_subset_smul_closedBallproof · cited by 1
- MontelSpace.finiteDimensional_of_normedSpaceproof · cited by 0