Theorems · Theorem · functional analysis
StrongDual.polar_singleton
∀ (𝕜 : Type u_4) [inst : NontriviallyNormedField 𝕜] {E : Type u_5} [inst_1 : AddCommMonoid E]
[inst_2 : TopologicalSpace E] [inst_3 : Module 𝕜 E] {a : E}, StrongDual.polar 𝕜 {a} = {x | ‖x a‖ ≤ 1}- Defined in
- Mathlib.Analysis.LocallyConvex.Polar
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.ofPredstatement and proof · cited by 6,101
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapproof · cited by 5,352
- StrongDualstatement and proof · cited by 459
Cited by1
Results whose statement or proof uses this declaration.
- StrongDual.mem_polar_singletonproof · cited by 0