Theorems · Theorem · functional analysis
NormedSpace.sInter_polar_eq_closedBall
∀ {𝕜 : Type u_3} {E : Type u_4} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] {r : ℝ},
0 < r → ⋂₀ (StrongDual.polar 𝕜 '' {F | F.Finite ∧ F ⊆ Metric.closedBall 0 r⁻¹}) = Metric.closedBall 0 r- Defined in
- Mathlib.Analysis.Normed.Module.Dual
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
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- Realstatement and proof · cited by 25,697
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
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- Set.ofPredstatement and proof · cited by 6,101
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- ContinuousLinearMapproof · cited by 5,352
- RCLikestatement and proof · cited by 2,829
- Set.Finitestatement and proof · cited by 1,814
- Metric.closedBallstatement and proof · cited by 704
- inv_invproof · cited by 494
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