Theorems · Theorem · functional analysis
NormedSpace.isVonNBounded_ball
∀ (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.ball 0 r)
- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 4 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.ballstatement · cited by 735
- Bornology.IsVonNBoundedstatement · cited by 136
- Metric.isBounded_ballproof · cited by 15
- NormedSpace.isVonNBounded_of_isBoundedproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- IsCompactOperator.image_ball_subset_compactproof · cited by 1
- NormedSpace.isBounded_iff_subset_smul_ballproof · cited by 1
- IsCompactOperator.isCompact_closure_image_ballproof · cited by 1
- exists_homeomorph_image_interior_closure_frontier_eq_unitBallproof · cited by 0