Theorems · Theorem · functional analysis
NormedSpace.closedBall_inv_subset_polar_closedBall
∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : SeminormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {r : ℝ}, Metric.closedBall 0 r⁻¹ ⊆ StrongDual.polar 𝕜 (Metric.closedBall 0 r)- Defined in
- Mathlib.Analysis.Normed.Module.Dual
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- LE.le.transproof · cited by 3,151
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- norm_nonnegproof · cited by 725
- Metric.closedBallstatement and proof · cited by 704
- StrongDualstatement and proof · cited by 459
- mul_le_mulproof · cited by 144
- dist_nonnegproof · cited by 126
Cited by1
Results whose statement or proof uses this declaration.
- NormedSpace.polar_closedBallproof · cited by 2