Theorems · Theorem · functional analysis
NormedSpace.isClosed_polar
∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : SeminormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] (s : Set E), IsClosed (StrongDual.polar 𝕜 s)- Defined in
- Mathlib.Analysis.Normed.Module.Dual
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- IsClosedstatement and proof · cited by 1,639
- StrongDualstatement · cited by 459
- LinearMap.flipproof · cited by 193
- IsClosed.preimageproof · cited by 138
- ContinuousLinearMap.continuousproof · cited by 124
- Continuous.normproof · cited by 45
Cited by1
Results whose statement or proof uses this declaration.
- NormedSpace.polar_closureproof · cited by 1