Theorems · Theorem · functional analysis

NormedSpace.polar_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 → StrongDual.polar 𝕜 (Metric.closedBall 0 r) = Metric.closedBall 0 r⁻¹

The polar of closed ball in a normed space E is the closed ball of the dual with inverse radius.

Defined in

Mathlib.Analysis.Normed.Module.Dual

Cited by

2 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedSpace